First slide

Mass Energy equivalence

Question

The minimum frequency of a $γ - r a y$ that causes a deuteron to disintegrate into a proton and a neutron is $[m_{d} = 2.0141 a m u, m_{p} = 1.0078 a m u, m_{n} = 1.0087 a m u]$

Moderate

A

$2.7 \times 10^{20} H z$
B

$5.4 \times 10^{20} H z$
C

$10.8 \times 10^{20} H z$
D

$21.6 \times 10^{20} H z$

Solution

(2)
Total mass of the product = 2.0165 amu which is greater than the mass of deuteron by 0.0024 amu. The extra mass must be provided by the energy of the photon. So the minimum possible frequency must be given by
$\begin{array}{l} v = \frac{0.0024 \times a m u \times c^{2}}{h} \\ = \frac{0.0024 \times 1.66 \times 10^{- 27} \times {(3 \times 10^{8})}^{2}}{6.625 \times 10^{- 34}} H z [1 a m u = 1.66 \times 10^{- 27} k g] \\ = 5.4 \times 10^{20} H z \end{array}$

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