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anygoal [31]
3 years ago
12

Determine the wavelength of the light absorbed when an electron in a hydrogen atom makes a transition from an orbital in which n

= 2 to an orbital in which n = 7.
Express the wavelength in nanometers to three significant figures.
Chemistry
1 answer:
wolverine [178]3 years ago
8 0

<u>Answer:</u> The wavelength of light is 3.97\times 10^2nm

<u>Explanation:</u>

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 = 7

n_i= Lower energy level = 2

Putting the values in above equation, we get:

\frac{1}{\lambda }=1.097\times 10^7m^{-1}\left(\frac{1}{2^2}-\frac{1}{7^2} \right )\\\\\lambda =\frac{1}{0.2518\times 10^7m^{-1}}=3.97\times 10^{-7}m

Converting this into nanometers, we use the conversion factor:

1m=10^9nm

So, 3.97\times 10^{-7}m\times (\frac{10^9nm}{1m})=3.97\times 10^2nm

Hence, the wavelength of light is 3.97\times 10^2nm

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