A nucleus of mass M emits a gamma-ray photon | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The energy of the $\gamma$-ray photon is $E_{\gamma} = h
u$.The momentum of the $\gamma$-ray photon is $p_{\gamma} = \frac{h
u}{c}$.By the law o

Vedclass · Accepted Answer

$h
u \left[1 + \frac{h
u}{2Mc^2}ight]$

Vedclass · Answer

(B) The energy of the $\gamma$-ray photon is $E_{\gamma} = h
u$.The momentum of the $\gamma$-ray photon is $p_{\gamma} = \frac{h
u}{c}$.By the law of conservation of momentum,the nucleus must recoil with an equal and opposite momentum $p_N = p_{\gamma} = \frac{h
u}{c}$.The kinetic energy of the recoiling nucleus is $K_N = \frac{p_N^2}{2M} = \frac{(h
u/c)^2}{2M} = \frac{(h
u)^2}{2Mc^2}$.The total loss in internal energy of the nucleus is the sum of the energy of the emitted photon and the kinetic energy of the recoiling nucleus:$\Delta E = E_{\gamma} + K_N = h
u + \frac{(h
u)^2}{2Mc^2} = h
u \left[1 + \frac{h
u}{2Mc^2}ight]$.

$A$ nucleus of mass $M$ emits a $\gamma$-ray photon of frequency $\nu$. The loss of internal energy by the nucleus is:

Similar Questions

The mass of an $\alpha$-particle is . . . . . . .

Which of the following elements has the maximum binding energy per nucleon?

The mass defect in a particular reaction is $0.4 \,g$.
The amount of energy liberated is $n \times 10^7 \,kWh$,where $n =$ . . . . . . . (speed of light $= 3 \times 10^8 \,m/s$)

$A$ nucleus of mass $ 20 u $ emits a $ \gamma $ photon of energy $ 6 MeV $. If the emission is assumed to occur when the nucleus is free and at rest, then the nucleus will have a kinetic energy nearest to (take $ 1 u = 1.6 \times 10^{-27} kg $): (in $keV$)

According to the mass-energy equivalence relation,$9 \times 10^{13} \text{ J}$ of energy can be converted into $\qquad$ maximum mass. [Speed of light $c = 3 \times 10^{8} \text{ m/s}$] (in $\text{ g}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module