Question

The wave length of radiation emitted when an electron in hydrogen atom drops from sixth orbit to fifth orbit is​

Answer 1

Answer:

the wave length of radiation

Answer 2

To find:

Wave length of radiation emitted when an electron in hydrogen atom drops from sixth orbit to fifth orbit ?

Calculation:

Applying Rydberg's Formula for wavelength of radiation due to electron's change in orbit:

$\therefore \: \dfrac{1}{ \lambda} = R \bigg[ \dfrac{1}{ { (n_{f})}^{2} } - \dfrac{1}{ {(n_{i})}^{2} } \bigg]$

Now , n_(f) = 5 and n_(i) = 6 (as per question):

$\implies\: \dfrac{1}{ \lambda} = R \bigg[ \dfrac{1}{ { (5)}^{2} } - \dfrac{1}{ {(6)}^{2} } \bigg]$

$\implies\: \dfrac{1}{ \lambda} = R \bigg[ \dfrac{1}{25} - \dfrac{1}{36} \bigg]$

$\implies\: \dfrac{1}{ \lambda} = R \bigg[ \dfrac{36 - 25}{25 \times 36} \bigg]$

$\implies\: \dfrac{1}{ \lambda} = R \bigg[ \dfrac{11}{25 \times 36} \bigg]$

$\implies\: \dfrac{1}{ \lambda} = R \bigg[ \dfrac{11}{900} \bigg]$

$\implies\: \lambda= \dfrac{900}{11 R}$

So , the wavelength is 900/(11R).