A beam of monochromatic light is used to exci | vedclass

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

Question

(B) For a hydrogen-like ion,the energy of an orbit is given by $E_n = -13.6 \frac{Z^2}{n^2} \; eV$.For $Li^{++}$,the atomic number $Z = 3$.The energy

Vedclass · Accepted Answer

$114$

Vedclass · Answer

(B) For a hydrogen-like ion,the energy of an orbit is given by $E_n = -13.6 \frac{Z^2}{n^2} \; eV$.For $Li^{++}$,the atomic number $Z = 3$.The energy of the first orbit $(n_1 = 1)$ is $E_1 = -13.6 	imes \frac{3^2}{1^2} = -13.6 	imes 9 = -122.4 \; eV$.The energy of the third orbit $(n_2 = 3)$ is $E_3 = -13.6 	imes \frac{3^2}{3^2} = -13.6 \; eV$.The energy required to excite the electron is $\Delta E = E_3 - E_1 = -13.6 - (-122.4) = 108.8 \; eV$.The wavelength $\lambda$ of the photon is given by $\lambda = \frac{hc}{\Delta E}$.Given $hc = 1242 \; eV \cdot nm = 12420 \; eV \cdot \mathring{A}$.$\lambda = \frac{12420 \; eV \cdot \mathring{A}}{108.8 \; eV} \approx 114.15 \; \mathring{A}$.Since $1 \; \mathring{A} = 10^{-10} \; m$,we have $\lambda \approx 114 	imes 10^{-10} \; m$.Thus,the value of $x$ is $114$.

$A$ beam of monochromatic light is used to excite the electron in $Li^{++}$ from the first orbit to the third orbit. The wavelength of monochromatic light is found to be $x \times 10^{-10} \; m$. The value of $x$ is $\dots$. [Given $hc = 1242 \; eV \cdot nm$]

Similar Questions

When the electron orbiting in a hydrogen atom in its ground state moves to the third excited state, the de-Broglie wavelength associated with it

The angular momentum for the electron in the first Bohr orbit is $L$. If the electron is assumed to revolve in the second orbit of a hydrogen atom,then the change in angular momentum will be:

The speed of an electron in the orbit of a hydrogen atom in the ground state is

Give the relationship between orbital radius and velocity of an electron for a hydrogen atom.

The wavelength of the first Balmer line caused by a transition from the $n=3$ level to the $n=2$ level in hydrogen is $\lambda_1$. The wavelength of the line caused by an electronic transition from $n=5$ to $n=3$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module