Question

The momentum of a photon of energy 1 MeV in kg m/s, will be

$0.33 space cross times space 10 to the power of 6$

$7 cross times 10 to the power of negative 24 end exponent$
$10 to the power of negative 22 end exponent$
$5 cross times 10 to the power of negative 22 end exponent$

Solution

5 cross times 10 to the power of negative 22 end exponent

Energy of photon is given by
$straight E space equals space hc over straight lambda$ ...(i)
Where h is Planck's constant, c the velocity of light and $straight lambda$ its wavelength.
de-Broglie wavelength is given by
$straight lambda space equals space straight h over straight p$ ...(ii)
p being momentum of photon.
From Eqs. (i) and (ii), we can have
   $straight E space equals space fraction numerator hc over denominator straight h divided by straight p end fraction space equals space pc$
$or space space space space space space space space space space space space space space space straight p space equals space straight E divided by straight c$
$Given comma space space straight E space equals space 1 space MeV space equals space 1 cross times 10 to the power of 6 cross times 1.6 cross times 10 to the power of negative 19 end exponent straight J$
   $straight C space equals 3 space cross times space 10 to the power of 8 space straight m divided by straight s$
Hence, after putting numerical values, we obtain
   $straight p equals fraction numerator 1 cross times 10 to the power of 6 cross times 1.6 cross times 10 to the power of negative 19 end exponent over denominator 3 cross times 10 to the power of 8 end fraction kgm divided by straight s space space space equals space 5 space cross times space 10 to the power of negative 22 end exponent space kgm divided by straight s$

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Wave Optics

The momentum of a photon of energy 1 MeV in kg m/s, will be

$0.33 space cross times space 10 to the power of 6$

$7 cross times 10 to the power of negative 24 end exponent$
$10 to the power of negative 22 end exponent$
$5 cross times 10 to the power of negative 22 end exponent$

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