JEE MAIN - Physics (2021 - 25th February Evening Shift - No. 25)
The wavelength of an X-ray beam is 10$$\mathop A\limits^o $$. The mass of a fictitious particle having the same energy as that of the X-ray photons is $${x \over 3}h$$ kg. The value of x is __________. (h = Planck's constant)
Answer
10
Explanation
Given wavelength of an x-ray beam = 10$$\mathop A\limits^o $$
$$ \because $$ E = $${{hc} \over \lambda } = m{c^2}$$
$$ \Rightarrow $$ m = $${h \over {c\lambda }}$$
The mass of a fictitious particle having the same energy as that of the x-ray photons = $${x \over 3}$$h kg
$$ \therefore $$ $${x \over 3}h = {h \over {c\lambda }}$$
$$x = {3 \over {c\lambda }}$$
$$ = {3 \over {3 \times {{10}^8} \times 10 \times {{10}^{ - 10}}}}$$
x = 10
$$ \because $$ E = $${{hc} \over \lambda } = m{c^2}$$
$$ \Rightarrow $$ m = $${h \over {c\lambda }}$$
The mass of a fictitious particle having the same energy as that of the x-ray photons = $${x \over 3}$$h kg
$$ \therefore $$ $${x \over 3}h = {h \over {c\lambda }}$$
$$x = {3 \over {c\lambda }}$$
$$ = {3 \over {3 \times {{10}^8} \times 10 \times {{10}^{ - 10}}}}$$
x = 10
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