Question

Calculate and compare the energies of two radiations one with a wavelength of 800 nm and other with wavelength of 400 nm.

Answer 1

Given, the two energy of radiations with wavelength ${ \lambda }_{ 1 } = 800nm$ and ${ \lambda }_{ 2 } = 400nm$

We know that, $E\quad =\quad h\nu$

E = energy

h = Planck’s constant $= 6.626\quad \times \quad { 10 }^{ -34 }\quad Js$

ν = frequency

${ \lambda }_{ 1 } = 400nm$ and ${ \lambda }_{ 2 } = 800nm$

C = Speed of light $= 3\quad \times \quad { 10 }^{ 8 }\quad m/s$

We also know,  

$\nu \quad =\quad \sfrac { c }{ \lambda }$

Substitute in the equation,

$E\quad =\quad h\quad \times \quad \frac { c }{ \lambda }$

For ${ \lambda }_{ 1 } = 400nm$

$E\quad =\quad \frac { 6.626\quad \times \quad { 10 }^{ -34 }\quad \times \quad 3\quad \times \quad { 10 }^{ 8 } }{ 400\quad \times \quad { 10 }^{ -9 } }$

$E\quad =\quad 5\quad \times \quad { 10 }^{ -19 }\quad J$

For ${ \lambda }_{ 2 } = 800nm$

$E = \frac { 6.626\quad \times \quad { 10 }^{ -34 }\quad \times \quad 3\quad \times \quad { 10 }^{ 8 } }{ 800\quad \times \quad { 10 }^{ -9 } }$

$E\quad =\quad 2.5\quad \times \quad { 10 }^{ -19 }\quad J$

Finally, the wavelength is inversely proportional to energy, where the radiation with wavelength 400nm is higher than the radiation with wavelength 800nm.

Answer 2

Given, the two energy of radiations with wavelength { \lambda }_{ 1 } = 800nmλ1​=800nm and { \lambda }_{ 2 } = 400nmλ2​=400nm

We know that, E\quad =\quad h\nuE=hν

E = energy

h = Planck’s constant = 6.626\quad \times \quad { 10 }^{ -34 }\quad Js=6.626×10−34Js

ν = frequency

{ \lambda }_{ 1 } = 400nmλ1​=400nm and { \lambda }_{ 2 } = 800nmλ2​=800nm

C = Speed of light = 3\quad \times \quad { 10 }^{ 8 }\quad m/s=3×108m/s

We also know,  



Substitute in the equation,

E\quad =\quad h\quad \times \quad \frac { c }{ \lambda }E=h×λc​

For { \lambda }_{ 1 } = 400nmλ1​=400nm

E\quad =\quad \frac { 6.626\quad \times \quad { 10 }^{ -34 }\quad \times \quad 3\quad \times \quad { 10 }^{ 8 } }{ 400\quad \times \quad { 10 }^{ -9 } }E=400×10−96.626×10−34×3×108​

E\quad =\quad 5\quad \times \quad { 10 }^{ -19 }\quad JE=5×10−19J

For { \lambda }_{ 2 } = 800nmλ2​=800nm

E = \frac { 6.626\quad \times \quad { 10 }^{ -34 }\quad \times \quad 3\quad \times \quad { 10 }^{ 8 } }{ 800\quad \times \quad { 10 }^{ -9 } }E=800×10−96.626×10−34×3×108​

E\quad =\quad 2.5\quad \times \quad { 10 }^{ -19 }\quad JE=2.5×10−19J

Finally, the wavelength is inversely proportional to energy, where the radiation with wavelength 400nm is higher than the radiation with wavelength 800nm.