The wavelength of a photon needed to remove a proton from a nucleus, to which it is bound with an energy of 1 MeV, is nearly (take \( hc=1240\,\mathrm{eV\,nm} \))
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 1.24\times10^{-3}\,\mathrm{nm} \)
To free the proton, the photon energy must equal the binding energy of 1 MeV. A photon of wavelength \( \lambda \) has energy \( E=hc/\lambda \), so \( \lambda=hc/E \).
\( E=1\,\mathrm{MeV}=10^{6}\,\mathrm{eV} \)
\( hc=1240\,\mathrm{eV\,nm} \)
\( \begin{aligned} \lambda &= \frac{hc}{E} \\ &= \frac{1240\,\mathrm{eV\,nm}}{10^{6}\,\mathrm{eV}} \\ &= 1.24\times10^{-3}\,\mathrm{nm} \end{aligned} \)