# HW Problem (Physics)

• In a fusion reaction, the nuclei of two atoms join to form a single atom of a different element. In such a reaction, a fraction of the rest energy of the original atoms is converted to kinetic energy of the reaction products. A fusion reaction that occurs in the Sun converts hydrogen to helium. Since electrons are not involved in the reaction, we focus on the nuclei.
Hydrogen and deuterium (heavy hydrogen) can react to form helium plus a high-energy photon called a gamma ray:

^1H + ^2H --> ^3He + gamma
Objects involved in the reaction:
Particle # of protons # of neutrons Charge Rest Mass (atomic mass units)
1H (proton) 1 0 +e 1.0073
2H (deuterium) 1 1 +e 2.0136
3He (helium) 2 1 +2e 3.0155
gamma ray 0 0 0 0

Although in most problems you solve in this course you should use values of constants rounded to 2 or 3 significant figures, in this problem you must keep at least 5 significant figures throughout your calculation. Problems involving mass changes require many significant figures because the changes in mass are small compared to the total mass. In this problem you must use the following values of constants, accurate to 5 significant figures:

Constant Value to 5 significant figures
c (speed of light) 2.9979e8 m/s
e (charge of a proton) 1.6022e-19 coulomb
atomic mass unit 1.6605e-27 kg
1/(4 pi epsilon_0) 8.9875e9 N·m2 /C2

The diagrams below represent different states in the fusion process: A proton (1H nucleus) and a deuteron (2H nucleus) start out far apart. An experimental apparatus shoots them toward each other (with equal and opposite momenta). If they get close enough to make actual contact with each other, they can react to form a helium-3 nucleus and a gamma ray (a high energy photon, which has kinetic energy but zero rest energy). Consider the system containing all particles. Work out the answers to the following questions on paper, using symbols (algebra), before plugging numbers into your calculator.

A: Bringing the particles together

Which diagram depicts the initial state in the process of bringing the particles together?

a

b

c

Which diagram depicts the final state in the process of bringing the particles together?

a

b

c

Compare the initial state and final states of the system. Which quantities have changed?

rest energy
potential energy
kinetic energy

The deuterium nucleus starts out with a kinetic energy of 1.71e-13 joules, and the proton starts out with a kinetic energy of 3.42e-13 joules. The radius of a proton is 0.9e-15 m; assume that if the particles touch, the distance between their centers will be twice that. What will be the total kinetic energy of both particles an instant before they touch? = ? Joules

B: Reaction to make helium

Now that the proton and the deuterium nucleus are touching, the reaction can occur.
Take the final state from the previous process to be the initial state of the system for this new process.
Which diagram depicts the final state?

a
b
c

Compare the initial state and final states of the system. Which quantities have changed?

kinetic energy
potential energy
rest energy

What is the kinetic energy of the reaction products (helium nucleus plus photon)? = ? Joules

C: Gain of kinetic energy:
What was the gain of kinetic energy in this reaction? (The products have more kinetic energy than the original particles did when they were far apart. How much more?) = ? Joules

D: Fusion as energy source
Kinetic energy can be used to drive motors and do other useful things. If a mole of hydrogen and a mole of deuterium underwent this fusion reaction, how much kinetic energy would be generated?

? Joules

(For comparison, around 1e6 joules are obtained from burning a mole of gasoline.)

• Oh my! Look at the problem là thấy sao chạy lòng dzòng rồi Sowie Ken, Kat hổng có giúp được gì, chỉ dzô đây make comment cho topic của Ken khỏi bị ế thôi . Bình tĩnh đọc lại textbook thì sẽ ra thôi Have a great weekend • @Kát: Ken đang bình tỉnh mà run nè .. • Lâu qua wên hết rồi ... đọc textbook & sample problems thì sẽ giải đc ...
A/ diagram c, b, mấy câu còn lại phải tính mới biết đc.
B/ diagram a
C/ after - before
D/ tinh for 1 mole

• mltr wrote:Lâu qua wên hết rồi ... đọc textbook & sample problems thì sẽ giải đc ...
A/ diagram c, b, mấy câu còn lại phải tính mới biết đc.
B/ diagram a
C/ after - before
D/ tinh for 1 mole

Mấy câu chọn hình thì Ken làm rồi . Còn những câu tính toán thì mờ mắt luôn .. . Giờ cũng due rồi .. hết cho làm nữa .. • Lòng Trắc Ẩn wrote:

Mấy câu chọn hình thì Ken làm rồi . Còn những câu tính toán thì mờ mắt luôn .. . Giờ cũng due rồi .. hết cho làm nữa .. Tới gần giờ due bài mới đi hỏi cách làm à   .

Lần sau hỏi bài TA or gọi phone cho bạn là nhanh nhứt & tỉ lệ đúng cao nhứt • Atmosphere at very high altitudes

In previous work we somewhat arbitrarily considered empty space to start at a height of 50 kilometers above the surface of the Earth.

(a) At this altitude, what is the density of the air as a fraction of the density at sea-level? (Assume that the temperature at this altitude is 7°C, and the mass of one mole of air is 29 g.)

500 times

greater than the density at sea-level
less than the density at sea-level

(b) Approximately how many air molecules are there in one cubic centimeter at this altitude?

? molecules/cm^3

(c) At what altitude is the air density one-millionth (10–6) that at sea level? (Assume that the temperature at this altitude is 7°C, and the mass of one mole of air is 29 g.)

? km • A nanoparticle containing 6 atoms can be modeled approximately as an Einstein solid of 18 independent oscillators. The evenly spaced energy levels of each oscillator are 3e-21 J apart. Use k = 1.4e-23 J/K.

(a) When the nanoparticle's energy is in the range 5(3e-21) J to 6(3e-21) J, what is the approximate temperature? (In order to keep precision for calculating the heat capacity, give the result to the nearest tenth of a degree.)

?

(b) When the nanoparticle's energy is in the range 8(3e-21) J to 9(3e-21) J, what is the approximate temperature? (In order to keep precision for calculating the heat capacity, give the result to the nearest tenth of a degree.)

?

(c) When the nanoparticle's energy is in the range 5(3e-21) J to 9(3e-21) J, what is the approximate heat capacity per atom?

?

Note that between parts (a) and (b) the average energy increased from "5.5 quanta" to "8.5 quanta". As a check, compare your result with the high temperature limit of 3k, where k = 1.4e-23 J/K.

Due tonight!  • Lòng Trắc Ẩn wrote:

Due tonight!  Due "tonight" có nghĩa là tối thứ năm, thứ sáu, thứ bảy, hay chủ nhựt dzị Due tối nào cũng chết Ken rồi, bay luôn cái weekend, khỏi gặp em  • hahaha physic bó tay .... có anh kia đang học giống ken mà giờ ảnh đang ôn final hổng dám hỏi giúp anh đâu .. sợ ổng chửi • Ra rồi ..

• Lòng Trắc Ẩn wrote:Ra rồi ..
thở phào nhẹ hõm hén • Lòng Trắc Ẩn wrote:Ra rồi ..

Dzị chiều chủ nhựt Ken đi nhà thờ được rồi  • katkatt wrote:
Lòng Trắc Ẩn wrote:Ra rồi ..

Dzị chiều chủ nhựt Ken đi nhà thờ được rồi  a ha .. Anh chỉ biết theo em khi nào dấu Amen! .. Mọi chi tiết, xin liên hệ: 