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Review Exam 1

Formulas

Time Dilation:

t t p

Length Contraction:

L

Relativistic Momentum:

p

Lp

mu 1

u2 c2

Formulas Relativistic Energy: Rest Energy:

E0 mc

2

mc

2

Total Energy: E K E0

1

u2 c2

Useful Formulas for Speed, Energy, and Momentum:

E hf

hc

f

c

E p c (mc ) 2

2 2

2 2

E pc,

for

E mc2

u pc c E

Photoelectric Effect:

mv2 eV0 hf 2 max Compton’s equation:

h 2 1 (1 cos ) mec Plank’s Law:

u ( )

2 5

8hc hc e kT

1

R T Stefan-Boltzman Radiation Law:

P AT

Stefan-Boltzman constant: 5.672 10

Wien’s displacement law: 3

max T cons tan t 2.898 10 m K Rayleigh-Jeans Law:

4

u ( ) kTn( ) 8kT

4

8

4 W

m2 K 4

m c 3 10 s 8

h 6.626 1034 J s 4.135 1015 eV s

Mass of electron : me 9.1094 1031kg 0.511 MeV

c2

Ch arg e of electron : e 1.6 1019 C Mass of the proton : m p 1.67 10 27 kg hc 1.9864 10 25 J m 1239.8eV nm

1eV 1.6022 1019 J

• Specific Heat:

• Latent Heat:

Q c mT

Q L m

Q mcT

Q Lm

• Work done by engine: Wengine Qnet Qh Qc

• Thermal Efficiency:

Qh Qc Qc e 1 Qh Qh Qh Weng

Typical Problems

Two identical twins Speedo and Goslo join a migration from the Earth to Planet X. It is 20.0 LY away in a reference frame in which both planets are in the rest. The twins, of the same age, departs at the same time on different spacecrafts. Speedo’s craft travels steadily at 0.950c, and Goslo’s at 0.750c. Calculate the age difference between the twins after Goslo’s spacecraft lands on Planet X. Which twin is the older?

A proton in high-energy accelerator moves with a speed c/2. Use the work kinetic energy theorem to find the work required to increase the speed to (a) 0.750c and (b) 0.995c.

In the constellation Orion we can observe two bright stars: Betelgeuse appears to glow red, while Rigel looks blue in color. Which star has a higher surface temperature? (λred=700nm; λblue=430nm)

Electrons are ejected from a metallic surface with speed ranging up to 4.60x105 m/s when light with a wavelength of 625 nm is used. What is the work function of the metal? What is the cutoff frequency of this surface?

A 0.110-nm photon collides with a stationary electron. After the collision, the electron moves forward and the photon recoils backward. Find the momentum and the kinetic energy of the electron. (Compton effect problem)

Find the power per unit area radiated from the surface of the sun in the wavelength range 600.0 to 605.0 nm

The power output of the Sun is 3.77×1026 W. How much mass is converted to energy in the Sun each second?

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Formulas

Time Dilation:

t t p

Length Contraction:

L

Relativistic Momentum:

p

Lp

mu 1

u2 c2

Formulas Relativistic Energy: Rest Energy:

E0 mc

2

mc

2

Total Energy: E K E0

1

u2 c2

Useful Formulas for Speed, Energy, and Momentum:

E hf

hc

f

c

E p c (mc ) 2

2 2

2 2

E pc,

for

E mc2

u pc c E

Photoelectric Effect:

mv2 eV0 hf 2 max Compton’s equation:

h 2 1 (1 cos ) mec Plank’s Law:

u ( )

2 5

8hc hc e kT

1

R T Stefan-Boltzman Radiation Law:

P AT

Stefan-Boltzman constant: 5.672 10

Wien’s displacement law: 3

max T cons tan t 2.898 10 m K Rayleigh-Jeans Law:

4

u ( ) kTn( ) 8kT

4

8

4 W

m2 K 4

m c 3 10 s 8

h 6.626 1034 J s 4.135 1015 eV s

Mass of electron : me 9.1094 1031kg 0.511 MeV

c2

Ch arg e of electron : e 1.6 1019 C Mass of the proton : m p 1.67 10 27 kg hc 1.9864 10 25 J m 1239.8eV nm

1eV 1.6022 1019 J

• Specific Heat:

• Latent Heat:

Q c mT

Q L m

Q mcT

Q Lm

• Work done by engine: Wengine Qnet Qh Qc

• Thermal Efficiency:

Qh Qc Qc e 1 Qh Qh Qh Weng

Typical Problems

Two identical twins Speedo and Goslo join a migration from the Earth to Planet X. It is 20.0 LY away in a reference frame in which both planets are in the rest. The twins, of the same age, departs at the same time on different spacecrafts. Speedo’s craft travels steadily at 0.950c, and Goslo’s at 0.750c. Calculate the age difference between the twins after Goslo’s spacecraft lands on Planet X. Which twin is the older?

A proton in high-energy accelerator moves with a speed c/2. Use the work kinetic energy theorem to find the work required to increase the speed to (a) 0.750c and (b) 0.995c.

In the constellation Orion we can observe two bright stars: Betelgeuse appears to glow red, while Rigel looks blue in color. Which star has a higher surface temperature? (λred=700nm; λblue=430nm)

Electrons are ejected from a metallic surface with speed ranging up to 4.60x105 m/s when light with a wavelength of 625 nm is used. What is the work function of the metal? What is the cutoff frequency of this surface?

A 0.110-nm photon collides with a stationary electron. After the collision, the electron moves forward and the photon recoils backward. Find the momentum and the kinetic energy of the electron. (Compton effect problem)

Find the power per unit area radiated from the surface of the sun in the wavelength range 600.0 to 605.0 nm

The power output of the Sun is 3.77×1026 W. How much mass is converted to energy in the Sun each second?