Question

a. Is a $4p\to 4s$transition allowed in sodium? If so, what is its wavelength (in nm)? If not, why not?

b. Is a$3d\to 4s$ transition allowed in sodium? If so, what is its wavelength (in nm)? If not, why not?

Short answer

a. The wavelength of $4p\to 4s$is $2.214\mu m$.

b. $3d\to 4s$transition not allowed .

Step-by-step solution

Part (a) step 1: Given Information

We need to find the wavelength of $4p\to 4s$.

Part (a) step 2: Simplify

Now, finding the wavelength for $4p\to 4s$transition in sodium.

Using formula:

$$\begin{gathered} \lambda =\frac{hc}{∆E} \\ \lambda =\frac{1240eVnm}{3.75ev-3.19eV} \\ \lambda =\frac{1240eVnm}{0.56eV} \\ \lambda =2214nm\to 2.214\mu m \end{gathered}$$

Part (b) step 1: Given Information

We need to find the wavelength of$3d\to 4s$.

Part (b) step 2 : Simplify

We have to find the wavelength for $3d\to 4s$transition in sodium.

Then, $3d\to 4s$the transition is not allowed because $∆l=2$violates the selection rule that requires$∆l=1$.