Question

A thorium nucleus of mass M=3.85×10−25kg is traveling in the +x-direction with vi=600m/s . The thorium nucleus then undergoes gamma decay, in which a gamma ray photon is emitted with wavelength λγ=0.004nm , in the +x-direction as shown in the figure. Which of the following gives the best estimate for the final velocity vf of the thorium nucleus after the photon is emitted?

Answer 1

The best estimate for the final velocity vf of the thorium nucleus after the photon is emitted is between 597 m/s and 603 m/s.

Option B is correct

The total momentum of the system before the decay is equal to the total momentum of the system after the decay.

Since the photon is emitted in the positive x-direction, the momentum of the photon will be in the negative x-direction.

The momentum of a photon is given by:

p = h/λ

p =
`1.656 *10^-^2^4` kg m/s

The total energy of the system (thorium nucleus and photon) before the decay is equal to the total energy of the system after the decay.

The energy of a photon is given by:

E = hc/λ

E =
`4.97 * 10^-^1^4` J

The change in momentum of the thorium nucleus can be calculated :

Δp = vf - vi

Δp =
`1.656 * 10^-^2^4` kg m/s

The change in energy of the thorium nucleus :

Δ
`E = vf^2/2 - vi^2/2`

Δ
`E = vf^2/2 - (600 m/s)^2/2`

`1.656 * 10^-^2^4 kg m/s = vf^2/2 - (600 m/s)^2/2`

vf = 597.6 m/s

or vf = 602.4 m/s

A thorium nucleus of mass M=3.85×10−25kg is traveling in the +x-direction with vi=600m/s . The thorium nucleus then undergoes gamma decay, in which a gamma ray photon is emitted with wavelength λγ=0.004nm , in the +x-direction as shown in the figure. Which of the following gives the best estimate for the final velocity vf of the thorium nucleus after the photon is emitted?

A. between 231 m/s and 342 m/s.

B. between 597 m/s and 603 m/s.

C. between 11.2 m/s and 123 m/s.