Question

The mass of a photon with wavelength 3.6˚A is .

• A. $9.1\times {10}^{-29}kg$
• B. $6.1\times {10}^{-29}kg$
• C. $8\times {10}^{-29}kg$

Answer 1

Answer: (B)

Step I:

$Here,\lambda =3.6\times {10}^{-10}m$

We know , de-Broglie wavelength

$\lambda$ = $\frac{h}{p}$ $\Rightarrow$ $\lambda$ = $\frac{h}{mv}$ $\Rightarrow m=$ $\frac{h}{\lambda v}$

Now,

$\lambda =3.6$ $\mathring{A}=3.6\times$ ${10}^{-10}m$

Velocity of photon = Velocity of light

$m=\frac{h}{\lambda v}$ = $\frac{6.626\times {10}^{-34}J{s}^{-1}}{(3.6\times {10}^{-10}m)(3\times {10}^{8}m{s}^{-1})}$

$=6.135\times {10}^{-29}kg$

Step II - Calculating the unit of mass

$Unitofmass=\frac{unitofplancksconstant}{unitofspeed\times wavelength}$

$m=\frac{Js}{m{s^{-1}\times m}^{}}$

$m=\frac{J}{{m^2}^{}}$

$Work=force\times distance$

$Work=mass\times acceleration\times distance$

$work=Kg\times {ms}^{-2}\times m$

$Joule=Kg{m}^2{s}^{-2}$

$HenceKg=\frac{Joule}{m^2{s}^{-2}}$

$Hencemass=0.6135\times {10}^{-32Kg}$

or

Mass

$6.1\times {10}^{-29}Kg$