Question

What is the wavelength (in nm) of a 3 eV photon?

Answer 1

Answer:The wavelength of a photon with energy 3.0 eV is 413.57 nm and it is for visible light. This wavelength is of ultraviolet light.

Explanation:

Answer 2

We are given –

• Energy of photon is = 3 eV

To find the wavelength of photon we have to use the Planck Expression.

$\qquad$ $\star\: \: \pink{\boxed{\frak{ E = hf}}}$

$\qquad$$\bf \longrightarrow E = hf$

$\qquad$$\sf \longrightarrow E = h \times \dfrac{c}{\lambda} \: \: \purple{\bigg(\because f = \dfrac{c}{\lambda}\bigg)}$

Where, E is the energy of photon and f is the frequency of photon & h's called Planck Constant.

$\qquad$$\sf \longrightarrow h = 6.63\times 10^{-34} \:Js$

$\qquad$ Speed of light, c =$\sf 3\times10^{8} \:m/s$

$\qquad\qquad\quad\underline{\sf{Substituting \ Values \ :}}$

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$\qquad$$\bf \longrightarrow E = h \times \dfrac{c}{\lambda}$

$\qquad$$\bf \longrightarrow \lambda = \dfrac{hc}{E}$

$\qquad$$\sf \longrightarrow \lambda = \dfrac{ 6.63\times 10^{-34}\times 3\times 10^{8}}{ 3eV}$

$\qquad$$\sf \longrightarrow \lambda = \dfrac{ 6.63\times 10^{-34}\times 3\times 10^{8}}{ 3 \times 1.6\times 10^{-19}}\: \:\purple{ \bigg(\because 1 eV= 1.6\times 10^{-19} J\bigg)}$

$\qquad$$\sf \longrightarrow \lambda = \dfrac{ 6.63 \times \cancel{3}\times 10^{-34+8}}{\cancel{3}\times 1.6\times 10^{-19}}$

$\qquad$$\sf \longrightarrow \lambda = \dfrac{ 6.63 \times 10^{-26}}{1.6\times 10^{-19}}$

$\qquad$$\sf \longrightarrow \lambda = 4.144 \times 10^{-26+19}$

$\qquad$$\sf \longrightarrow \lambda = 4.144 \times 10^{-7}$

$\qquad$$\sf \longrightarrow \lambda = 4.144\times 10^{-7}\: m$

$\qquad$$\sf \longrightarrow \lambda = 4.144 \times 10^{-7}\times 10^{9} \: nm\: \: \purple{\bigg(\because 1m = 10^9\: nm \bigg)}$

$\qquad$$\sf \longrightarrow \lambda = 4.144 \times 10^{-7+9}\: nm$

$\qquad$$\sf \longrightarrow \lambda = 4.144 \times 10^{2}\: nm$

$\qquad$$\pink{\bf \longrightarrow \lambda = 414.4\: nm}$

• Henceforth, wavelength will be 414.4nm.