Question

The rest mass of a proton is 1.67 * 10-27
10-27 kg. What
should be the maximum wavelength of a photon to
produce a proton-antiproton pair? Ans. 6.6 x 10-6 Å.
​

Answer 1

Answer:

The maximum wavelength of the photon will be 6.6×10⁻⁶A°.

Explanation:

The maximum wavelength of a photon to produce proton-antiproton pair is calculated as,

$\lambda=\frac{h}{mc}$         (1)

Where,

λ=maximum wavelength of the photon

h=plancks constant=6.6×10⁻³⁴ Joule-second

m=mass of the proton-antiproton pair

c=speed of light=3×10⁸m/s

From the question we have,

Mass of proton(M)=1.67×10⁻²⁷kg

The mass of the antiproton is the same as that of the proton. So,

$m=2M$

$m=2\times 1.67\times 10^-^2^7$    (2)

By substituting the required values in equation (1) we get;

$\lambda=\frac{6.6\times 10^-^3^4}{2\times 1.67\times 10^-^2^7\times 3\times 10^8}$

$\lambda=0.658\times 10^-^1^5$

$\lambda\approx 6.6\times 10^-^6A\textdegree$

Hence, the maximum wavelength of the photon will be 6.6×10⁻⁶A°.

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