This is a collection of exercises to be carried out on the web or on the classroom computers. Their intent is to show you a range of numerical answers associated with different physical phenomena; these are the type of calculations which are carried out in the problem-solving type physics courses. In the case of these exercises, the actual calculations are done by the computer but it is hoped that the exercises will help you become accustomed to the computer as a tool and a source of information.

这些练习可以在网络上或教室的电脑上进行。其目的是向你展示与不同物理现象相关的各种数值答案；这些就是问题解决型物理课程中进行的计算类型。在这些练习中，实际的计算由计算机完成，但希望这些练习能帮助你逐渐适应计算机作为工具和信息来源的角色。

网络或课堂练习

Note about entering numbers in calculations: When you enter a number in one of the calculations in HyperPhysics, you then just click anywhere outside the box to make sure the transaction is complete and the number is taken. If you need to edit the number, it is usually easiest to just double-click in the data entry box. That will turn the field dark, and any number you type will replace the previous number.

关于在计算中输入数字的说明：当你在HyperPhysics中的某个计算中输入一个数字时，只需点击框外的任何地方以确保交易完成，数字将被采纳。如果需要编辑数字，通常最简单的方法是双击数据输入框。这会将字段变暗，你输入的任何数字都将替换之前的数字。

The items which you can change are in the boxes (launch speed and time). You can calculate the height and speed at any time, and the peak height associated with your chosen launch velocity is displayed.

你可以更改的是框中的项目（发射速度和时间）。你可以计算任意时刻的高度和速度，与你选择的发射速度相关的最高高度也会显示出来。

1. If you toss a ball upward at a speed of 30 m/s, its maximum height will be _________ meters.
2. For a ball tossed at 30 m/s, the speed after 1 second will be _________ m/s and its height at that time will be __________ meters.
3. After 2 seconds the speed will be __________ m/s and the height ________ m.
4. After 3 seconds the speed will be __________ m/s and the height ________ m.
5. After 5 seconds the speed will be __________ m/s and the height ________ m.
6. After 6 seconds the speed will be __________ m/s and the height ________ m.

1. 如果你以30 m/s的速度向上抛一个球，它的最大高度将是________米。2. 对于以30 m/s速度抛出的球，1秒后速度将是________m/s，此时高度为________米。3. 2秒后速度将是________m/s，高度________米。4. 3秒后速度将是________m/s，高度________米。5. 5秒后速度将是________m/s，高度________米。6. 6秒后速度将是________m/s，高度________米。

Exercise 2: Trajectory
The intent of this exercise is to calculate a baseball trajectory by determining the height of the ball at different distances. The scenario is that of a baseball hit at an angle of 45° and a speed of 100 miles/hr (44.7 m/s). The fence is 12 ft (3.7m) high and is200 meters away from home plate. Your task is to plot the trajectory of the baseball at 20 meter intervals, assuming that it was hit at a height of 1 meter, and determine whether it clears the fence.

练习2：轨迹本练习的目的是通过计算不同距离处球的高度来计算棒球的轨迹。情景是：一球以45°角击出，速度为100英里/小时（44.7 m/s）。围栏高12英尺（3.7米），距离本垒200米。你的任务是按20米的间隔绘制棒球的轨迹，假设球是在1米高处击出的，并确定它是否能越过围栏。

练习3：重量计算

1 kg 的物体的重量是 ______ 牛 = ______ 磅。

2. If an object weighs 50 lbs on the surface of the Earth, its mass is _______kg.

如果一个物体在地球表面的重量是50磅，其质量是______千克。

如果一个人的重量是150磅，在公制单位中应为____牛顿。

4. The mass unit of the U.S. common sytem is the slug. If an object has a mass of one slug, then it will have a mass of _______kg and would weight ______ lbs.

4. 美国常用单位制中的质量单位是slug。如果一个物体的质量为1 slug，那么它的质量将是______kg，重量为______lbs。

1. If a mass of 1 kg were traveling at 10 m/s and were brought to rest in 1 second, the average force necessary would be __________ N.

1. 如果一个1千克的物体以10米/秒的速度运动，并在1秒内停止，所需的平均力为__________牛。

2. If the same mass under the same conditions were brought to rest in one one-hundredth of a sec (0.01s) the average force necessary would be _______N.

如果在相同条件下，同样的质量在0.01秒内停下来，所需的平均力将是______N。

3. If a 0.15 kg baseball traveling toward you at 30 m/s were stopped by your glove in 0.1 s, the average force on your hand would be ________ N.

如果一个质量为0.15 kg的棒球以30 m/s的速度朝你飞来，被你的手套在0.1 s内停下，那么对你手的平均力将是______ N。

4. If a 0.15 kg baseball traveling toward you at 30 m/s were struck by your bat and sent outward at 30 m/s in a collision which lasted 0.01 s, the average force on the ball would be _________ N. But if you stuck your bat out to bunt the ball and just stopped it in 0.01 s, the force on the ball would be only ______N.

4. 如果一个0.15 kg的棒球正以30 m/s的速度向你飞来，被你的球棒击中后以30 m/s的速度向外飞出，在持续0.01 s的碰撞中，球所受的平均力为______N。但如果你将球棒伸出去击球，仅在0.01 s内将球停住，球所受的力则仅为______N。

练习5：向心力和向心加速度

1. If you were swinging a 0.5 kg mass around your head on a string in a circle of radius 0.5 meters at a speed of 5 m/s, the required tension in the string would be ________N.

如果你用一根长0.5米的绳子将0.5千克的质量在头旁做圆周运动，速度为5米每秒，那么绳子的张力应为______牛。

如果将速度加倍到10 m/s，张力将是______ N。

3. If at a speed of 5 m/s you pulled the string in to a 0.25 m radius,
the tension would be _________ N.

如果以5 m/s的速度将绳子拉入半径为0.25 m的圆周，张力将是______ N。

4. On a flat curve of radius 500 m, a 1000 kg car tries to make the curve at 25 m/s (about 56 mi/hr). If the maximum friction force is 80% of the car's weight, can it make the curve? At what maximum speed can it make the curve? (Hint: first calculate the weight of the car.)

4. 在半径为500米的平弯道上，一辆1000千克的汽车试图以25米/秒（约56英里/小时）的速度转弯。如果最大摩擦力是汽车重量的80%，它能否成功转弯？它能以多大的最大速度转弯？（提示：首先计算汽车的重量。）

练习6：轨道速度与轨道重量

1. In an orbit 200 kilometers above the surface of the Earth, the orbit velocity is about ________ mi/hr, and the time to orbit the Earth is about ______ min. At that altitude, the force of gravity has fallen to about _______ times the force at the surface of the Earth.

在距地球表面200公里的轨道上，轨道速度约为______英里/小时，绕地球运行的时间约为______分钟。在该高度，重力的力已降至地球表面的力的约______倍。

2. To create a geosynchronous satellite (one which stays above the same point on the Earth for communication purposes), you would have to put it out at about _________ x the radius of the Earth. (Hint: If it stays above your head all the time, what is its orbital period?)

要创建一个地球同步卫星（它始终停留在地球上的同一位置以用于通信目的），你必须将其放在大约 _________ 倍地球半径之外。（提示：如果它始终停留在你头顶上空，它的轨道周期是多少？）

3. The 24 satellites of the Global Positioning Service are in orbits about 11000 miles above the Earth (17.7 x 106 meters). These satellites circle the Earth in aobut ________ hours.

3. 全球定位服务的24颗卫星位于地球上方约11000英里（17.7×10⁶米）的轨道上。这些卫星绕地球运行约______小时。

4. Joe weighs 220 lb and would like to get down to 200 lb. How high above the Earth would he have to go to decrease his weight by 10%?

4. 约翰重220磅，希望减重到200磅。他需要离地球多高才能使自己的重量减少10%？

大气力应为“大气的力”。修正后的中文为：大气的力

1. The force of normal atmospheric pressure on one square foot of the Earth's surface is ____________ pounds.

地球表面每平方英尺的大气压力的力是__________磅。

2. The force of 1 atmosphere pressure on the top of a car which is 4ft x 4ft is _______ pounds. Why does it not crush the car?

2. 1 个大气压对汽车顶部（4 英尺 × 4 英尺）的力是多少磅？为什么它不会压碎汽车？

3. The force of 1 atmosphere of pressure on the roof of a house which measures 60ft by 30 ft is ______________ pounds.

1 个大气压对一间60英尺乘30英尺房屋屋顶施加的力是________磅。

4. If a passing tornado lowers the outside air pressure to 13.7 lb/in2 while the pressure inside the above house remains at 1 atmos, what will be the net upward force on the roof of the house? (Hint calculate the force with 1 atmos and then with 13.7 lb/in2 and take the difference.)

4. 如果一场经过的龙卷风将室外的空气压力降至13.7 lb/in²，而屋内上方的气压仍保持在1个大气压，那么屋顶上将产生多大的净向上力？（提示：先计算1个大气压和13.7 lb/in²的力，再求其差值。）

练习8：汽车碰撞中的力

1. If a 3200 lb car traveling at 30 mi/hr strikes the tree and stops in a distance of 1 foot, the average impact force on the car would be ______ tons.

如果一辆重3200磅的汽车以30英里/小时的速度撞树并停在1英尺的距离内，汽车上平均冲击力为____吨。

2. If the car above were built more sturdily so that it stopped in 0.5 feet, the average impact force on the car would be ______ tons.

如果上面的汽车更坚固，使其在0.5英尺内停止，汽车所受的平均冲击力将是____吨。

3. The average force on a 160 lb driver who was stopped with the car in part 1 above in a distance of 1 foot, the force on the driver would be _______ tons. (Hint: Put in 160 lb in the box labeled Weight of Car - it works on any weight.)

3. 一辆重160磅的司机在上述第1部分中以1英尺的距离停止时，作用在司机身上的平均力为____吨。（提示：将160磅放入标有‘汽车重量’的框中，它适用于任何重量。）

4. If the 160 lb driver, traveling at 30 mi/hr, had no seatbelt on so that he was stopped by the steering column and windshield in a distance of 0.2 feet, the average force on the driver would be ________ tons.

如果160磅的司机以30英里/小时的速度行驶，没有安全带，于是被方向盘和挡风玻璃在0.2英尺的距离内停下，司机所受的平均力为________吨。

练习9：温度刻度

If you double-click on any of the closed boxes and change the number, then clicking outside the box will calculate the equivalent temperatures in the other scales.

如果你双击任何一个封闭的框并更改数字，那么点击框外时会计算其他温度刻度的等效温度。

1. The temperature of this room has typically been 21°C lately. That is ______°F

这间房间的温度最近通常为21°C，即______°F

2. 那是______°C。

3. 那是______°F。

绝对零度（0 K）等于________℃和________°F。

5. There is a temperature at which the Celsius temperature is equal to the Fahrenheit temperature. At that temperature ________°C = ________°F. (Hint: Find it by plugging in different numbers and changing them until the temperatures approach each other.)

5. 存在一个温度，使得摄氏温度等于华氏温度。在该温度下 ________°C = ________°F。（提示：通过代入不同数值并调整直到温度接近相等。）

练习10：热与比热容。

1. If in the lab you heated 400 grams of copper from 20°C to 95°C, and the specific heat of copper is 0.092 cal/gm°C, the heat required is Q = _______cal.

在实验室中，若将400克铜从20°C加热到95°C，且铜的比热为0.092 cal/g°C，则所需热量Q = _______cal。

2. If you put that amount of heat into 100 grams of water at 20°C, it will raise its temperature by _________°C.

如果你将这种热量加到100克20°C的水中，其温度将升高________°C。

3. If you heat 100 grams of water from 20°C to 21°C, the heat required is Q=_______ calories.

如果将100克水从20°C加热到21°C，所需热量为Q=_______卡路里。

练习11：理想气体定律

Set the initial and final volumes to 1 liter, and the initial and final pressures to 1 atmosphere.

将初始体积和终体积设为1升，初始压力和终压力设为1个大气压。

1. If the initial temperature is 0°C and the final temperature is 20°C, then in absolute temperature the initial and final values will be _____K and _____K.

如果初始温度是0°C，最终温度是20°C，那么在绝对温度下，初始和最终的值将是______K和______K。

2. If the pressure is constant at 1 atmos, you start with 1 liter and you increase the temperature from 0 to 20°C, the final volume will be ______liters.

如果压力保持在1个大气压，你从1升开始，将温度从0°C升高到20°C，最终体积将是____升。

3. If both initial and final temperatures are 0°C, initial volume 1 liter, initial pressure 1 atmosphere, then the increase of pressure from 1 to 2 atmospheres will result in a final volume of _______ liters.

如果初始温度和最终温度都是0°C，初始体积为1升，初始压力为1个大气压，那么压力从1个大气压增加到2个大气压将导致最终体积为______升。

4. If you keep the volume of gas at 1 liter and start with 1 atmosphere of pressure at 0°C, a temperature of _____K = ______°C will be required to raise the pressure to 2 atmospheres.

如果保持气体体积为1升，从1个大气压和0°C开始，要将压力提高到2个大气压，温度需达到_____K = ______°C。

Exercise 12: Maximum efficiency allowed by the Second Law of Thermodynamics: the Carnot cycle.

练习12：第二热力学定律允许的最大效率：卡诺循环。

1. If a coal-fired power plant operated at a temperature of 650 K and exhausted its waste heat at 300 K, then its maximum efficiency would be ________%.

如果一台燃煤发电厂的运行温度为650 K，而其废热排放温度为300 K，那么其最大效率将是________%。

2. If you operated near the softening point of the steel reactor vessel at 850K, the ideal efficiency is increased to _______%.

2. 如果你在钢反应堆容器的软化点附近操作，理想效率会增加到_____%。

3. If an ocean thermal generator makes use of the fact that surface seawater is at about 300 k and deeper water is at about 290 K, the maximum efficiency of the generator would be ________%.

如果海洋热发电机利用表层海水约300 K，深层海水约290 K的温差，其最大效率将为________%。

4. If exhaust fumes from your car are at 310 K, and the environment is at 300 K, then you could judge the maximum efficiency of any energy reclamation project for the energy in the exhaust would be at most ________% efficient.
(Hint: The higher temperature is considered to be the source of the energy and the lower temperature is the temperature of the cold reservoir in the heat engine model.)

如果汽车尾气温度为310 K，而环境温度为300 K，那么你可以判断任何用于回收尾气中能量的项目的最大效率最多为______%。（提示：较高的温度被视为能量源，较低的温度是热机模型中的低温库温度。）

练习13：电 circuits

1. If 120 volts is applied to a 60 ohm resistor, the current will be _______ amps.

若将120伏电压加到一个60欧姆的电阻上，电流将是______安。

2. In order to double the current, the resistance will have to be changed to ____ ohms.

为了使电流加倍，电阻必须改变为____欧姆。

3. To get 5 amperes of current to flow through an 8 ohm loudspeaker coil, you will have to apply ________ volts.

要使5安培的电流通过一个8欧姆的扬声器线圈流动，必须施加________伏特。

4. If you have 0.1 ohms of resistance at your car's battery terminals because of accumulated corrosion and your car's starter causes a current of 85 amperes to flow, how much of the 12 volt battery's voltage is dropping across the corrosion at the terminal? (Hint: The 0.1 ohms is in series with the starter motor, and any voltage drop across that resistance is subtracted from the voltage applied to the starter.)

4. 如果由于积累的腐蚀，你汽车的电池端子处有0.1欧姆的电阻，而汽车的启动电机导致85安培的电流流过，那么12伏电池的电压中有多少是在终端的腐蚀上损失的？（提示：0.1欧姆的电阻与启动电机是串联的，该电阻上的电压降会从施加在启动电机上的电压中扣除。）

假设以下内容使用标准的家用交流电压120伏：

1. The amount of power which can be obtained from a household circuit which has a 20 ampere breaker is _________ watts.

家庭电路中具有20安熔断器的电路所能获得的功率是________瓦特。

2. If you want to limit the power to your stereo amplifier to 500 watts, you should put in a fuse to limit the current to _______ amperes.

如果你想将立体声放大器的功率限制在500瓦，你应该安装一个熔断器以将电流限制在______安培。

3. Using 15 ampere fuses in your house will limit the power from each circuit to ________ watts.

在家中使用15安熔断器将限制每个电路的功率为________瓦。

4. If you wanted to supply 40 watts of power to a toy train which operated off a 6 volt transformer, the required current would be _________ amps.

如果你想要通过一个6伏特的变压器为一辆玩具火车提供40瓦的功率，所需电流为________安培。

练习15：串联和并联电路

假设以下情况为120伏特供电

1. If you placed a 10 ohm resistance in series with a 40 ohm resistor, the voltage across the 10 ohm resistor would be ________ volts. But if you put it in parallel with the 40 ohms, the voltage would be _______ volts.

如果将一个10欧姆的电阻与一个40欧姆的电阻串联，那么10欧姆电阻两端的电压将是______伏。但如果将其并联在40欧姆电阻上，电压将是______伏。

2. A pair of 40 ohm resistors is placed in parallel where they draw ______ amps of current from the power supply. If they are placed in series they will draw only ______ amps.

两只40欧姆的电阻并联时，会从电源中吸取______安的电流。若串联则只能吸取______安的电流。

3. A 40 ohms resistor by itself will draw _______ amps of current from the 120 volt supply. If you put a 2 ohm resistor in series with it the total current will be _______ amps. If you put a 2 ohm resistor in parallel with it the total current will be _______ amps.

3. 40欧姆的电阻单独使用时，会从120伏的电源中吸取______安的电流。如果将2欧姆的电阻与它串联，总电流将是______安。如果将2欧姆的电阻与它并联，总电流将是______安。

练习16：波的计算

1. What is the wavelength in meters of the electromagnetic carrier wave transmitted by the radio station WSB AM at 750 kHz? 1 kHz =10³ Hz and the speed of light is 3 x 10⁸ m/s.

无线电电台WSB AM在750 kHz频率上传输的电磁载波波长是多少米？1 kHz=10³ Hz，光速为3×10⁸ m/s。

2. What is the wavelength in meters of the electromagnetic carrier wave transmitted by GSU's WRAS at 88.5 MHz ? 1 MHz = 10⁶ Hz

2. GSU的WRAS发射的电磁波波长是多少米？1 MHz = 10⁶ Hz

3. If a sound is produced at the orchestra standard frequency of 440 Hz, at a temperature where the speed of sound is 345 m/s, what is the wavelength of the sound produced?

如果在标准音乐会音高440 Hz下产生声音，温度下声音的速率为345 m/s，所产生的声音的波长是多少？

4. If the limits of human hearing are 20 Hz to 20,000 Hz, what are the sound wavelengths associated with these extremes. You may use 345 m/s for the speed of sound.

4. 如果人类的听觉范围是20 Hz到20000 Hz，这些极值对应的声波波长是多少？你可以使用345 m/s作为声速。

Exercise 17: Open air column resonance
1. If a flute constitutes an open air column, how long must the air column be if it is to produce a frequency at middle-C, 261 Hz?

练习17：开放空气柱的共振 1. 如果 flute 构成一个开放空气柱，那么要使其产生中音C（261 Hz）的频率，空气柱的长度必须多长？

2. An open-ended organ pipe is to be constructed to sound the note A= 55 Hz, one octave above the bottom note on the piano. How long must the air column be?

要构造一个开口的管风琴管，使其能发出A=55 Hz的音调，该音调比钢琴最低音高一个八度。空气柱必须有多长？

练习18: 闭合空气柱共振

1. A clarinet acts as a closed-ended air column. If its bottom note has a frequency of 130 Hz, how long is the column?

1. 一种圆号相当于一个封闭的空气柱。如果它的最低音频率为130 Hz，这个空气柱有多长？

2. The ear canal responds most strongly to frequencies around 3700 Hz because that is the lowest resonant frequency of the canal. If the canal acts like a closed-ended cylinder, how long is the ear canal?

耳道对约3700 Hz的频率响应最强，因为这是耳道的最低共振频率。如果耳道可以看作是一个封闭的圆柱体，那么耳道有多长？

3. If the top resonance of the water tube resonance unit is at a column length of 8 cm when a tuning fork of frequency 1024 Hz , what is the corresponding speed of sound?

如果水柱共振器的最高共振频率对应于8厘米的柱长，当使用频率为1024 Hz的音叉时，求相应的声速？

Exercise 19: Formation of real images
1. If a camera lens has a focal length of f = 5 cm, at what image distance from the lens must the film be placed to form an image of an object which is 500 cm from the lens?

练习19：实像的形成 1. 如果一个相机镜头的焦距为 f = 5 cm，当物体距离镜头500 cm时， film 应放置在距离镜头多少厘米处以形成物体的像？

2. If the object is moved closer to the camera lens ( to 100 cm) what is the distance to the film from the lens?

如果物体被移近相机镜头（至100厘米），则镜头到胶片的距离是多少？

3. If you want to take a picture of a flower at only 20 cm from the lens, what lens-to-film image distance would be required? (This probably would require and extension tube).

如果你想拍摄一朵距离镜头仅20厘米的花，所需的镜头到底片的像距是多少？（这可能需要使用延长管。）

4. In a slide projector the slide is placed very close to the focal length of the lens. If you want to project an image 5 meters away from a f=5cm slide projector lens, where would you have to put the slide (object distance)?

在幻灯机中，幻灯片被放置在透镜的焦距非常接近的位置。如果你希望用一个f=5cm的透镜将图像投射到5米远处，幻灯片（物距）应该放在哪里？

练习20：虚像的形成

1. If you are looking through a divergine lens of focal length f = -20 cm at an object which is 40 cm away from the lens, at what distance from the lens would the image appear to be?

如果你通过一个焦距为 f = -20 cm 的发散透镜观察一个距离透镜 40 cm 的物体，图像会出现在距离透镜多远的位置？

练习21：更多的虚拟像

If the object distance is smaller than the focal length of a magnifying lens, then the image will be virtual, on the same side of the lens as the object and further away.

如果物体距离小于放大透镜的焦距，那么像将是虚像，位于透镜与物体同侧，并且更远离透镜。

1. If you use a magnifier of focal length f=10 cm to look at an object which is at 5 cm from the lens, where will the image appear to be? What will be the magnification?

如果你使用一个焦距为 f=10 厘米的放大镜来观察一个距离透镜 5 厘米的物体，图像会出现在哪里？放大率是多少？

2. If you put the object closer to the focal length, at 9 cm from the lens, where will the image be and what is its magnification?

如果将物体放在距离透镜9厘米处，像会出现在哪里？其放大率是多少？

Exercise 22: Atomic Spectra
Radiation of all the types in the electromagnetic spectrum can come from the atoms of different elements. A rough classification of some of the types of radiation by wavelength is:
Infrared   > 750 nm
Visible   400 - 750 nm
Ultraviolet   10-400 nm
Xrays   < 10 nm
(An approximate classification of spectral colors: Violet (380-435nm), Blue(435-500 nm), Cyan (500-520 nm), Green (520-565 nm), Yellow (565- 590 nm), Orange (590-625 nm), Red (625-740 nm).
1. If the electron in a hydrogen atom (Z=1) makes a transition from n=2 to n=1, the wavelength of the radiation will be _______ nm, which is in the __________ part of the electromagnetic spectrum.
2. If the electron in a hydrogen atom (Z=1) makes a transition from n=3 to n=2, the wavelength of the radiation will be _______ nm, which is in the __________ part of the electromagnetic spectrum.
1. If the electron in a hydrogen atom (Z=1) makes a transition from n=4 to n=3, the wavelength of the radiation will be _______ nm, which is in the __________ part of the electromagnetic spectrum.
1. If the electron in a oxygen atom (Z=8) makes a transition from n=2 to n=1, the wavelength of the radiation will be _______ nm, which is in the __________ part of the electromagnetic spectrum.

练习22：原子光谱电磁谱中所有类型的辐射都可以来自不同元素的原子。按波长大致分类的一些辐射类型是：红外线>750 nm 可见光 400-750 nm 紫外线 10-400 nm X射线<10 nm（近似颜色光谱分类：紫（380-435nm），蓝（435-500 nm），青（500-520 nm），绿（520-565 nm），黄（565-590 nm），橙（590-625 nm），红（625-740 nm）。1. 如果氢原子（Z=1）中的电子从n=2跃迁到n=1，辐射的波长将是______ nm，位于电磁谱的________部分。2. 如果氢原子（Z=1）中的电子从n=3跃迁到n=2，辐射的波长将是______ nm，位于电磁谱的________部分。3. 如果氢原子（Z=1）中的电子从n=4跃迁到n=3，辐射的波长将是______ nm，位于电磁谱的________部分。4. 如果氧原子（Z=8）中的电子从n=2跃迁到n=1，辐射的波长将是______ nm，位于电磁谱的________部分。

Exercise 23: Radioactive half-life
1. If the half-life of a certain radioisotope is 1 year, what fraction of it will remain after 3 years? _____________
2. For carbon-14 with a half-life of 5730 years, how long will it take to decay to one-tenth of its original activity? _____________
3. Iodine-131 has a half-life of 8 days. If a given contamination is considered tolerable when it has decayed to one-thousandth (0.001) of its original value, how long would that take? _____________
4. Cesium-137, the most insidious of the contaminants released at Chernobyl, has a half-life of 30 years. If it must reduce to one-thousandth of its initial value, how long would that take? _____________

练习23：放射性半衰期 1. 如果某种放射性同位素的半衰期为1年，那么3年后剩余的分数是多少？_____________ 2. 对于碳-14，其半衰期为5730年，要衰变到原始活度的十分之一，需要多长时间？_____________ 3. 碘-131的半衰期为8天。如果某次污染被认为可接受的条件是其衰变到原始值的千分之一（0.001），那么需要多长时间？_____________ 4. 铯-137，是切尔诺贝利事故中释放出的最危险的污染物之一，其半衰期为30年。如果它必须衰变到初始值的千分之一，需要多长时间？_____________