The kinetic energy of an electron in the seco | vedclass

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

Question

(C) For a hydrogen atom,the radius of the $n^{th}$ Bohr orbit is given by $r_n = n^2 a_0$,where $a_0$ is the Bohr radius.For the second orbit $(n = 2)

Vedclass · Accepted Answer

$\frac{h^2}{32\pi^2 m a_0^2}$

Vedclass · Answer

(C) For a hydrogen atom,the radius of the $n^{th}$ Bohr orbit is given by $r_n = n^2 a_0$,where $a_0$ is the Bohr radius.For the second orbit $(n = 2)$,$r_2 = 2^2 a_0 = 4 a_0$.The velocity of an electron in the $n^{th}$ orbit is $v_n = \frac{nh}{2\pi m r_n}$.Substituting $r_n = n^2 a_0$,we get $v_n = \frac{nh}{2\pi m (n^2 a_0)} = \frac{h}{2\pi m n a_0}$.For $n = 2$,$v_2 = \frac{h}{2\pi m (2) a_0} = \frac{h}{4\pi m a_0}$.The kinetic energy $(KE)$ is given by $KE = \frac{1}{2} m v_2^2$.$KE = \frac{1}{2} m \left( \frac{h}{4\pi m a_0} \right)^2 = \frac{1}{2} m \left( \frac{h^2}{16\pi^2 m^2 a_0^2} \right) = \frac{h^2}{32\pi^2 m a_0^2}$.

The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is = ....... (Bohr radius $a_0$)

Similar Questions

What is the maximum wavelength in the Lyman series of $He^{+}$ ion?

Which of the following statements is $NOT$ true about Rutherford's atomic model?

The energy of a photon is $3 \times 10^{-12} \ erg$. What is its wavelength in $nm$? $(h = 6.62 \times 10^{-27} \ erg \cdot s; \ c = 3 \times 10^{10} \ cm/s)$

The value of Planck's constant is $6.63 \times 10^{-34} \ J \ s$. The velocity of light is $3.0 \times 10^8 \ m \ s^{-1}$. Which value is closest to the wavelength in nanometres of a quantum of light with frequency of $8 \times 10^{15} \ s^{-1}$?

If the wavelength of an electromagnetic radiation is $2000 \ \text{Å}$, what is its energy in ergs?

Vedclass Test Series

Exam Paper Generator

Online Exam Module