Question

The $5d\to 3p$transition in the emission spectrum of sodium has a wavelength of $499nm$.What is the energy of the$5d$state ?

Short answer

The energy of $5d$state is$4.589eV$.

Step-by-step solution

Given Information

We have been given that the emission spectrum of sodium has a wavelength of $499nm$in $5d\to 3p$transition. We need to find energy of $5d$state.

Simplify 

We are given with $\lambda =499nm$and $E_{3p}=2.104eV$, where $\lambda$is wavelength and $E_{3p}$is energy of $3p$state. We also know about energy equation , which can be written as :

localid="1650300462496" $E_{5d\to 3p}=\frac{hc}{\lambda }$,localid="1650300525081" $\lambda$here is wavelength and we know the standard value of localid="1650300529926" $h$and localid="1650300534619" $c$

By substituting the values we get,

$E_{5d\to 3p}=\frac{1240eVnm}{499nm}=2.485eV$

To find the value of localid="1650300538851" $E_{5d}$,we can use the equation ,localid="1650300543949" $E_{5d}=E_{3p}+E_{5d\to 3p}$

We will substitute the values on right hand side of the equation,

localid="1650300548403" $E_{5d}=2.104eV+2.485eV=4.589eV$