1. State Bohr’s postulate to define stable orbits in hydrogen ato… - Vidyadip

Question

State Bohr’s postulate to define stable orbits in hydrogen atom. How does de Broglie’s hypothesis explain the stability of these orbits?
A hydrogen atom initially in the ground state absorbs a photon which excites it to the n = 4 level. Estimate the frequency of the photon.

✓

Answer

Quantum condition:

The electrons are permitted to circulate only in those orbits in which the angular momentum of an electron is an integralmultiple of $\frac{\text{h}}{2\pi};$ h being Plancks constant. Therefore, for any permitted orbit.

$\text{L}=\text{mvr}=\frac{\text{nh}}{2\pi},\ \text{n}=1, 2,3, .....$

where L,m and v are the angular momentum,mass and speed of the electron, r is the radius of the permitted orbit and n is positive integer called principal quantum number, The above equation is Bohrs famous quantum condition.

Stationary orbits:

While revolving in the permissible orbits, an electron does not radiate energy. These non-radiating orbits are called stationary orbits.

According to de-Broglie, the circumference of $n^{th}$ circular orbit in which electron is revolving is given by:

$2\pi\text{r}_{\text{n}}=\text{n}\lambda\ .....(\text{i})$

where $\lambda=$ wavelength of wave emitted by electron

also, by de-Broglies hypothesis

$\lambda=\frac{\text{h}}{\text{mv}}\ ....(\text{ii})$

From (i) and (ii)

$2\pi\text{r}_{\text{n}}=\frac{\text{nh}}{\text{mv}}$

$\therefore\ \text{mvr}_{\text{n}}=\frac{\text{nh}}{2\pi}$

$\frac{1}{\lambda}=\text{R}\Big(\frac{1}{\text{n}^2_1}-\frac{1}{\text{n}^2_2}\Big)$

Here:

$n_1 = 1$

$n_2 = 4$

$\frac{1}{\lambda}=\text{R}\Big(1-\frac{1}{4}\Big)$

$\frac{1}{\lambda}=\frac{3}{4}\text{R}$

$\lambda=\frac{4}{3\text{R}}$

Now, $\text{c}=\text{f}\lambda$

$\text{f}=\frac{\text{c}}{\lambda}=\frac{4\text{c}}{3\text{R}}$

Where c = speed of light in vacuum $= 3 \times 10^8m/ s.$

R = Rhydberg constant $= 1.09 \times 10^7m^{-1}.$

$\text{f}=\frac{4\times3\times10^8}{3\times1.09\times10^7}$

$\text{f}=36.69\text{Hz}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Atoms→Atoms — all question types→Physics STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Find the angle of deviation suffered by the light ray shown in figure. The refractive index $\mu=1.5$ for the prism material.

The following table gives the output of a two input logic gate.

Identify the logic gate and draw its logic symbol.
If the output of this gate is fed as input to a NOT gate, name the new logic gate so formed.

A	B	Y
0	0	1
1	0	1
0	1	1
1	1	0

Boron has two stable isotopes, $^{10}_5\text{B }\text{ and }\ ^{11}_5\text{B}.$ Their respective masses are 10.01294 u and 11.00931 u, and the atomic mass of boron is 10.811 u. Find the abundances of $^{10}_5\text{B }\text{ and }\ ^{11}_5\text{B}.$

When we heat an object, it expands. Is work done by the object in this process ? Is heat given to the object equal to the increase in its internal energy?

A particle moves in a circle of radius 1.0cm at a speed given by v = 2.0t where v is in cm/s and t in seconds.

Find the radial acceleration of the particle at t = 1s.
Find the tangential acceleration at t = 1s.
Find the magnitude of the acceleration at t = 1s.

A sample of paramagnetic salt contains $2.0 \times 10^{24}$ atomic dipoles each of dipole moment $1.5 \times 10^{-23} \mathrm{~J} \mathrm{~T}^{-1}$. The sample is placed under a homogeneous magnetic field of 0.64 T , and cooled to a temperature of 4.2 K . The degree of magnetic saturation achieved is equal to $15 \%$. What is the total dipole moment of the sample for a magnetic field of 0.98 T and a temperature of 2.8 K ? (Assume Curie's law)

A narrow beam of light passes through a slab obliquely and is then received by an eye. The index of refraction of the material in the slab fluctuates slowly with time. How will it appear to the eye? The twinkling of stars has a similar explanation.

Deduce the expression for the torque $\overrightarrow{\tau}$ acting on a planar loop of area $\overrightarrow{\text{A}}$ and carrying current I placed in a uniform magnetic field $\overrightarrow{\text{B}}.$ If the loop is free to rotate, what would be its orientation in stable equilibrium?

Write the basic features of the photon picture of electromagnetic radiation on which Einstein's photoelectric equation is based.

Let $A_1A_2A_3 A_4 A_5 A_6 A_1$ be a regular hexagon. Write the x-components of the vectors represented by the six sides taken in order. Use the fact that the resultant of these six vectors is zero, to prove that$\cos0+\cos\frac{\pi}{3}+\cos\frac{2\pi}{3}+\cos\frac{3\pi}{3}+\cos\frac{4\pi}{3}+\cos\frac{5\pi}{3}=0.$
Use the known cosine values to verify the result.