Question

Find energy of each of the photons which:
(i) correspond to light of frequency 3×$10^{15}$ Hz.
(ii) have wavelength of $0.50 \AA$.

Answer 1

(i) Energy of photon is given by the expression

$E\quad =\quad hv$

$h\quad =\quad planks\quad constant\quad =\quad 6.626\quad \times \quad { 10 }^{ -34 }\quad Js$

$v\quad =\quad frequnecy\quad of\quad light\quad =\quad 3\quad \times \quad 1{ 0 }^{ 15 }\quad Hz$

Substituting all the values in the equation,

$E\quad =\quad (6.626\quad \times \quad { 10 }^{ -34 }\quad Js)(3\quad \times \quad 1{ 0 }^{ 15 }Hz)$

$E\quad =\quad 1.988\quad \times \quad 1{ 0 }^{ -18 }\quad J$

(ii) Energy (E) of a photon having wavelength $(\lambda )$ is given by the following expression.

$E\quad =\quad \frac { hc }{ \lambda }$

$h\quad =\quad planks\quad constant\quad =\quad 6.626\quad \times { 10 }^{ -34 }\quad Js$

$c\quad =\quad velocity\quad of\quad light\quad in\quad vaccum\quad =\quad 3\quad \times \quad { 10 }^{ 8 }\quad m/s$

Substituting the values in the given expression E

$E\quad =\quad \frac { (6.626\quad \times \quad { 10 }^{ -34 }\quad Js)(3\quad \times \quad { 10 }^{ 8 }\quad m/s) }{ 0.50\quad \times \quad { 10 }^{ -10 } } \quad =\quad 3.976\quad \times \quad { 10 }^{ -15 }J$

$E\quad =\quad 3.976\quad \times \quad { 10 }^{ -15 }\quad J$