Question

Consider the transition from the energy levels n = 3 to n = 5. What is the wavelength associated with this transition, in nm?

Answer 1

Answer: The wavelength of transition is 1281 nm

Explanation:

To calculate the wavelength of light, we use Rydberg's Equation:

$\frac{1}{\lambda}=R_H\left(\frac{1}{n_i^2}-\frac{1}{n_f^2} \right )$

Where,

$\lambda$ = Wavelength of radiation

$R_H$ = Rydberg's Constant  = $1.097\times 10^7m^{-1}$

$n_f$ = Higher energy level = 5

$n_i$= Lower energy level = 3

Putting the values in above equation, we get:

$\frac{1}{\lambda }=1.097\times 10^7m^{-1}\left(\frac{1}{3^2}-\frac{1}{5^2} \right )\\\\\lambda =\frac{9\times 25}{0.2518\times 10^7m^{-1}\times 16}=12.81\times 10^{-7}m$

Converting this into nanometers, we use the conversion factor:

$1m=10^9nm$

So, $12.81\times 10^{-7}m\times (\frac{10^9nm}{1m})=1281nm$

Hence, the wavelength of light is 1281 nm

Answer 2

Answer:

wavelength is 1301.8 nm

Explanation:

Given data

energy levels n = 3 to n = 5

to find out

What is the wavelength

solution

we know wavelength formula that is given below

1/wavelength = RH(1/n1² - 1/n2²)

here we know RH value is  10973731.6 m^(-1)

so

wavelength = 1 / RH(1/n1² - 1/n2²)

wavelength = 1 / 10973731.6 (1/3² - 1/5²)

wavelength = 1.3018 ×10^-6 m

wavelength is 1301.8 nm