Doppler Shift If an atom is moving when it emits light, the frequency v that is

Question

Doppler Shift If an atom is moving when it emits light, the frequency v that is observed in the lab will be Doppler shifted relative to the frequency v_0 in the atom's rest frame. For light that travels along the r-axis, the lab frequency is given by v = v_0 times (1 + v_x/c), correct to first order in inverse powers of the speed of light c. Here v_x is the atom's x-component of velocity Take the light source to be sodium vapor at T = 10^3K, and take v_0 = 5.09 times 10^14 Hz. The mass of a sodium atom is 3.82 times 10^-26 kg. Imagine that a spectroscope is oriented along the x-axis. (a) Determine the probability distribution P(v)dv for receiving a photon in the frequency range v to v + dv. The probability distribution is to be normalized to unity. (For convenience, allow |v_x| to exceed the speed of light, but provide justification for that mathematical approximation.) (b) what is the root mean square spread of lab frequencies? That is, what is((v - v_0)^2)^1/2 How large is that spread in comparison with the natural frequency v_0?

Explanation / Answer

a) probability distribution , P(v)dv =   vo2 * sqrt(1 - vx2/c2) dv

b) root mean square spread of lab frequencies =>

v' =    sqrt(3 * 8.314 * 1000/3.82 * 10-26)

      = 8.08 * 1014 Hz

=> minimum lab frequency =   8.08 * 1014 - 5.09 * 1014

                                           = 2.99 * 1014 Hz

=>   maximum lab frequency =   8.08 * 1014 + 5.09 * 1014

                                           = 13.17 * 1014 Hz

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.