When a hydrogen atom is excited by radiation | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The energy of the incident photon is $E = \frac{hc}{\lambda} = \frac{12400 \, 	ext{eV} \cdot \mathring{A}}{975 \, \mathring{A}} \approx 12.718 \,

Vedclass · Accepted Answer

$18787 \, \mathring{A}, 975 \, \mathring{A}$

Vedclass · Answer

(B) The energy of the incident photon is $E = \frac{hc}{\lambda} = \frac{12400 \, 	ext{eV} \cdot \mathring{A}}{975 \, \mathring{A}} \approx 12.718 \, 	ext{eV}$.This energy corresponds to the transition from the ground state $(n=1)$ to the $n=4$ state,as $E_4 - E_1 = -0.85 - (-13.6) = 12.75 \, 	ext{eV}$.When the atom de-excites from $n=4$,the possible transitions are $4 	o 3, 4 	o 2, 4 	o 1, 3 	o 2, 3 	o 1, 2 	o 1$.The maximum wavelength corresponds to the minimum energy transition,which is $4 	o 3$.$E_{4 	o 3} = E_4 - E_3 = -0.85 - (-1.51) = 0.66 \, 	ext{eV}$.$\lambda_{max} = \frac{12400}{0.66} \approx 18787.8 \, \mathring{A}$.The minimum wavelength corresponds to the maximum energy transition,which is $4 	o 1$.$E_{4 	o 1} = 12.75 \, 	ext{eV}$.$\lambda_{min} = \frac{12400}{12.75} \approx 972.5 \, \mathring{A} \approx 975 \, \mathring{A}$ (as per the excitation energy).Thus,the values are $18787 \, \mathring{A}$ and $975 \, \mathring{A}$.

When a hydrogen atom is excited by radiation of wavelength $975 \, \mathring{A}$,the maximum and minimum wavelengths of the emitted radiation are respectively:

Similar Questions

What is the ratio of the time periods of an electron in the $n = 2$ and $n = 1$ orbits of a hydrogen atom (in $:1$)?

Using Bohr's atomic model,derive an equation for the radius of the $n^{th}$ orbit of an electron.

The energy level diagram for a hydrogen-like atom is shown in the figure. The radius of its first Bohr orbit is

The time period of revolution of an electron in the $n^{\text{th}}$ orbit in a hydrogen-like atom is given by $T = \frac{T_0 n^a}{Z^b}$,where $Z$ is the atomic number. Identify the correct values for $T_0$,$a$,and $b$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module