Question

A series of line in athe spectrum of atomic hydrogen lie at the frequencies shown below. What is the frequencey of the next line in the series? Explain how you reach your answer.

4.5669 X 10¹⁴ s^-1

6.1653 X 10¹⁴ s^-1

6.8905 X 10¹⁴ s^-1

Answer 1

Solution:

We know the Balmer equation to calculate frequecies of line in the series.

We have given 3 frequencies but we will use last one and we will see that this is the frequency of which which integer

By balmer equation;

v = [1/4 - 1/n²] * 329 * 10¹⁵ S-1

we have v = 6.8905 * 10¹⁴

Put in the above equation we get,

6.8905 * 10¹⁴ = [1/4 - 1/n²] * 329 *10¹⁵

[1/4 - 1/n²] = 0.2094

1/n² = 0.25-0.002094

n = 2

Now lets find out next n = 3 frequency,

v = [1/4 - 1/n²] * 329 * 10¹⁵

= [0.25 - 1/9] * 329 *10¹⁵

= 456.89 * 10¹⁴