 Home

Codex Wiki

List of universities

University of Oxford

Course of the University of Oxford

Undergraduate course of the University of Oxford

Physics course of the University of Oxford

Year 3 of the physics course of the University of Oxford

Atomic and laser physics course of the University of Oxford

Past exam of the atomic and laser physics course of the University of Oxford

2021

{c}

Take the initial ground-state <chemical atom> at rest in the laboratory. The incident <photon> has <energy> $h\nu$ and <momentum> $h\nu/c$. The excited <chemical atom> has <rest mass> $M+\Delta M$ and must carry that <momentum>. <Conservation of energy> and <conservation of momentum> give
$$
Mc^2+h\nu=\sqrt{(M+\Delta M)^2c^4+(h\nu)^2}.
$$
Squaring cancels the photon-energy square:
$$
M^2c^4+2Mc^2h\nu=(M+\Delta M)^2c^4.
$$
Consequently
$$
\boxed{\nu=\frac{\Delta Mc^2}{h}\left(1+\frac{\Delta M}{2M}\right)
=\nu_{\rm int}+\frac{h\nu_{\rm int}^2}{2Mc^2},\qquad
h\nu_{\rm int}=\Delta Mc^2.}
$$
The extra positive term is the <photon absorption recoil correction> and supplies atomic <recoil energy>. The formula is exact for the initially stationary isolated <chemical atom>; it does not assume $\Delta M/M\ll1$. Initial and final <chemical atoms> cannot both remain at rest during single-<photon> absorption without another body taking <momentum>.

Solution

Past exam of the atomic and laser physics course of the University of Oxford / 2021 / 4 / d / Solution

Past exam of the atomic and laser physics course of the University of Oxford / 2021 / 4 / d / Solution

 Ancestors (12)

 Discussion (0)

 Articles by others on the same topic (0)

Past exam of the atomic and laser physics course of the University of Oxford / 2021 / 4 / d / Solution

 Ancestors (12)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)