Question

find the wavelength of a photon having energy of 250ev​

Answer 1

Quantization of Light and the Planck-Einstein Relation

The Planck-Einstein Relation is:

$E = h\nu$

Where

E = Energy of a single photon

h = Planck's constant

$\nu$ = Frequency

What it implies is that light energy is quantized. The energy of light is present in the form of small discrete packets called quanta. For light, we call them Photons.

So, Photons are the small discrete packets of light energy.

The energy contained in a given photon depends on its frequency, as given by the formula above.

Photons, being light, travel at the speed of c = 299792458 m/s in vacuum.

The simple relation between frequency and wavelength is:

$c = \lambda \nu \\\\\\ \implies \nu = \dfrac{c}{\lambda}$

So, the Planck-Einstein Relation can be re-written as:

$E = h\nu \\\\\\ \implies \boxed{E = \dfrac{hc}{\lambda}}$

Here, we know the value of the constants:

$h = 6.626 \times 10^{-34}\ J\, s \\\\ c = 2.99792458 \times 10^8\ m/s \approx 3\times 10^8\ m/s$

The Energy is 250 eV.

The relation between electron-volt and joule is:

$1\ eV = 1.602 \times 10^{-19}\ J$

So, the Energy is:

$E = 250\ eV = 250\times 1.602\times 10^{-19}\ J = 400.5 \times 10^{-19}\ J$

We can now use the formula to find the wavelength:

$\displaystyle E=\frac{hc}{\lambda} \\\\\\ \implies \lambda = \frac{hc}{E} \\\\\\ \implies \lambda = \frac{6.626\times 10^{-34} \times 2.99792458 \times 10^8}{400.5\times 10^{-19}}\ m \\\\\\ \implies \lambda \approx 4.9599 \times 10^{-9} \ m \\\\\\ \implies \Large\boxed{\lambda \approx 4.96 \times 10^{-9}\ m}$

Thus, The Wavelength of the Photon is 4.96 nm.

Answer 2

Answer:

The wavelength of the photon is 4.96 nm