Question

Calculate the wavelength of a photon that has three times as much energy as that of a photon of
wavelength 779 nm?
(A) 460 nm
(B) 360 nm
(C) 260 nm
(D) 560 nm​

Answer 1

To find:

the wavelength of a photon that has three times as much energy as that of a photon of

wavelength 779 nm.

Calculation:

General expression is energy of a wave:

$\boxed{ \sf{E = \dfrac{hc}{ \lambda} }}$

So, we can say that energy of wave is inversely proportional to wavelength.

$\boxed{ \sf{E \propto \dfrac{1}{ \lambda} }}$

So, taking corresponding ratios:

$\rm{ \therefore \: \dfrac{E1}{E2} = \dfrac{ \lambda2}{ \lambda1} }$

$\rm{ = > \: \dfrac{E1}{3(E1)} = \dfrac{ \lambda2}{779} }$

$\rm{ = > \lambda2 = \dfrac{779}{3} }$

$\rm{ = > \lambda2 \approx 260 \: nm}$

So, final answer is:

$\boxed{ \bf{ \lambda2 \approx 260 \: nm}}$