Advertisements
Advertisements
प्रश्न
The radius of the innermost electron orbit of a hydrogen atom is 5.3 × 10−11 m. What are the radii of the n = 2 and n = 3 orbits?
Advertisements
उत्तर
The radius of the innermost orbit of a hydrogen atom, r1 = 5.3 × 10−11 m
Let r2 be the radius of the orbit at n = 2. It is related to the radius of the innermost orbit as:
r2 = (n)2r1
= (2)2 × 5.3 × 10−11
= 4 × 5.3 × 10−11
= 2.12 × 10−10 m
For n = 3, we can write the corresponding electron radius as:
r3 = (n)2r1
= (3)2 × 5.3 × 10−11
= 9 × 5.3 × 10−11
= 4.77 × 10−10 m
Hence, the radii of an electron for n = 2 and n = 3 orbits are 2.12 × 10−10 m and 4.77 × 10−10 m, respectively.
APPEARS IN
संबंधित प्रश्न
Obtain an expression for the radius of Bohr orbit for H-atom.
(i) State Bohr's quantization condition for defining stationary orbits. How does the de Broglie hypothesis explain the stationary orbits?
(ii) Find the relation between three wavelengths λ1, λ2 and λ3 from the energy-level diagram shown below.
Lifetimes of the molecules in the excited states are often measured by using pulsed radiation source of duration nearly in the nanosecond range. If the radiation source has a duration of 2 ns and the number of photons emitted during the pulse source is 2.5 × 1015, calculate the energy of the source.
Using Bohr’s postulates, obtain the expression for the total energy of the electron in the stationary states of the hydrogen atom. Hence draw the energy level diagram showing how the line spectra corresponding to Balmer series occur due to transition between energy levels.
The Bohr radius is given by `a_0 = (∈_0h^2)/{pime^2}`. Verify that the RHS has dimensions of length.
Suppose in an imaginary world the angular momentum is quantized to be even integral multiples of h/2π. What is the longest possible wavelength emitted by hydrogen atoms in visible range in such a world according to Bohr's model?
Draw energy level diagram for a hydrogen atom, showing the first four energy levels corresponding to n=1, 2, 3 and 4. Show transitions responsible for:
(i) Absorption spectrum of Lyman series.
(ii) The emission spectrum of the Balmer series.
Use Bohr’s model of hydrogen atom to obtain the relationship between the angular momentum and the magnetic moment of the revolving electron.
A particle has a mass of 0.002 kg and uncertainty in its velocity is 9.2 × 10−6 m/s, then uncertainty in position is ≥ ____________.
(h = 6.6 × 10−34 J s)
Ratio of longest to shortest wavelength in Balmer series is ______.
Derive an expression for the frequency of radiation emitted when a hydrogen atom de-excites from level n to level (n – 1). Also show that for large values of n, this frequency equals to classical frequency of revolution of an electron.
The mass of a H-atom is less than the sum of the masses of a proton and electron. Why is this?
The value of angular momentum for He+ ion in the first Bohr orbit is ______.
Find the ratio of energies of photons produced due to transition of an election of hydrogen atom from its (i) second permitted energy level to the first level. and (ii) the highest permitted energy level to the first permitted level.
In Bohr's theory of hydrogen atom, the electron jumps from higher orbit n to lower orbit p. The wavelength will be minimum for the transition ______.
What is meant by ionisation energy?
Specify the transition of an electron in the wavelength of the line in the Bohr model of the hydrogen atom which gives rise to the spectral line of the highest wavelength ______.
How much is the angular momentum of an electron when it is orbiting in the second Bohr orbit of hydrogen atom?
The de Broglie wavelength of an electron in the first Bohr’s orbit of hydrogen atom is equal to ______.
