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  • If a stationary electron gets annihilated due to the association with a stationary positron (hypothetically), the wavelength of the resulting radiation will be where <img alt="m_0=" src="

If a stationary electron gets annihilated due to the association with a stationary positron (hypothetically), the wavelength of the resulting radiation will be

where m_0= rest mass of an electron (or positron) 

              c=\text { speed of light }

Option: 1

\frac{h}{m_0 c}


Option: 2

\frac{2 h}{m_0 c}


Option: 3

\frac{h}{2 m_0 c}


Option: 4

None of these


Answers (1)

best_answer

Conserving the momenta of the system just before and after the event (anhiliation) we see that two identical photons will be resulted and travel in opposited directions with equal magnitude of momenta and energy \frac{\text { hc }}{\lambda} where \lambda= wavelength of radiation. 

Conservation of energy yields,

\begin{aligned} & \frac{\mathrm{hc}}{\lambda}+\frac{\mathrm{hc}}{\lambda}=\mathrm{m}_{0} \mathrm{c}^2+\mathrm{m}_{0} \mathrm{c}^2 \\ & \Rightarrow \quad \frac{\mathrm{hc}}{\lambda}=\mathrm{m}_{0} \mathrm{c}^2 \quad \Rightarrow \quad \lambda=\frac{\mathrm{h}}{\mathrm{m}_0 \mathrm{c}} \end{aligned}

Posted by

HARSH KANKARIA

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