**PHY1161
**

December 11, 2002

**1. [25 pts]** (**27.2**) A flashbulb goes off at the origins as the origins of our usual reference frames A and B coincide. Frames A and B have a relative speed of 0.6 c along their x-axes. A wavefront travels along the x-axis as observed in B. What time is recorded in B as this wavefront reaches x_{B} = 1,000 m? Use these values of x_{B} and t_{B} to calculate the coordinates x_{A} and t_{A} that describe this event in A. Then use these values to calculate the speed of light in reference frame A ( v_{light} = x_{A}/t_{A}).

To find time t_{B} we just use the definition of velocity

v = c = x_{B}/t_{B}

t_{B} = x_{B}/c

t_{B} = 3.333 x 10^{–6} s

Of course, we also have

x_{B} = 1000 m

Now we can apply the Lorentz Transformations to find x_{A} and t_{A},

**x _{A} = 2 000 m**

And, indeed, this

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This provides a more direct application of our velocity transformation equation,

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**3. [10 pts]**

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**4. [15 pts]**

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**5. [15 pts]** (**29.1**) Calculate the __second__ wavelength of the Balmer series for hydrogen and tell what color it is.

Balmer Series for Hydrogen

R = 1.097 x 10^{7} m ^{–1}, Rydberg constant

For n = 4 we have

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**6. [20 pts]** (**29.16**) In state “A” the energy of an atom is – 4.56 eV and in state “B” its energy is – 7.89 eV.

a) What is the energy of the photon emitted in the transition from “A” to “B”?

b) What is the wavelength of this photon?

c) What color is the light of this photon?