Question

Two photons of same frequency are produced due to the annhiliation of a proton and antiproton. Wave length of the proton so produced is:

• (A) $1.1\times {10}^{-14}\mathrm{m}$
• (B) $1.3\times {10}^{-15}\mathrm{m}$
• (C) $1.7\times {10}^{-17}\mathrm{m}$
• (D) $1.9\times {10}^{-19}\mathrm{m}$

Answer 1

The Correct Option is B

Explanation:
Given:Two photons of same frequency are produced due to the annhiliation of a proton and antiproton.We know that:$c=3\times {10}^8$Mass of a proton = $1.67\times {10}^{-27}$$E=m{c}^2$Put the values in above formula.$E=(2\times 1.67\times {10}^{-27})\times {(3\times {10}^8)}^2\mathrm{J}$$=3.006\times {10}^{-10}\mathrm{J}$Also We know that:$2h\nu =E$ or $2h\frac{c}{\lambda }=E$$\therefore \lambda =\frac{2hc}{E}$Put the values in above formula.$=\frac{2\times 6.62\times {10}^{-34}\times 3\times {10}^8}{3.006\times {10}^{-10}}\mathrm{m}$$=1.323\times {10}^{-15}\mathrm{m}$Hence, the correct option is (B).