An atom of mass M which is in the state of rest emits a photon of wavelength λ. As a result, the atom will deflect with the kinetic energy equal to (h is Planck's constant)

Question

An atom of mass M which is in the state of rest emits a photon of wavelength λ. As a result, the atom will deflect with the kinetic energy equal to (h is Planck's constant) (A)  (h2/Mλ 2) (B)  (1/2)(h2/Mλ 2) (C)  (h/Mλ )  (D)  (1/2)(h/Mλ )

Tardigrade Admin · Accepted Answer

Momentum of photon, p=(h/λ) Kinetic energy of photon of mass M, K=(p2/2 M) or K=(h2/2 M λ2)

Q. An atom of mass $M$ which is in the state of rest emits a photon of wavelength $λ$ . As a result, the atom will deflect with the kinetic energy equal to $(h$ is Planck's constant)

$\frac{h ^{2}}{M λ ^{2}}$

$\frac{1}{2} \frac{h ^{2}}{M λ ^{2}}$

$\frac{h}{M λ}$

$\frac{1}{2} \frac{h}{M λ}$

Momentum of photon, $p = \frac{h}{λ}$
Kinetic energy of photon of mass
$M, K = \frac{p ^{2}}{2 M}$
or $K = \frac{h ^{2}}{2 M λ ^{2}}$

Q. An atom of mass M which is in the state of rest emits a photon of wavelength λ. As a result, the atom will deflect with the kinetic energy equal to (h is Planck's constant)

Mλ2h2​

21​Mλ2h2​

Mλh​

21​Mλh​