Advertisements
Advertisements
प्रश्न
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?
Advertisements
उत्तर
In the imaginary world, the angular momentum is quantized to be an even integral multiple of h/2 π.
Therefore, the quantum numbers that are allowed are n1 = 2 and n2 = 4
We have the longest possible wavelength for minimum energy.
Energy of the light emitted (E) is given by
`E = 13.6 (1/n_1^2 - 1/n_2^2)`
`E = 13.6 [ 1/(2)^2 - 1/(4)^2]`
`E = 13.6 (1/4 - 1/16)`
`E = (13.6xx12)/64 = 2.55 eV`
Equating the calculated energy with that of photon, we get
2.55 eV = `(hc)/lamda`
`lamda = (hc)/2.55 = 1242/2.55 nm`
= 487.05 nm= 487 nm
APPEARS IN
संबंधित प्रश्न
How many electrons in an atom may have the following quantum numbers?
n = 4, `m_s = -1/2`
Which of the following parameters are the same for all hydrogen-like atoms and ions in their ground states?
In a laser tube, all the photons
A positive ion having just one electron ejects it if a photon of wavelength 228 Å or less is absorbed by it. Identify the ion.
A neutron moving with a speed υ strikes a hydrogen atom in ground state moving towards it with the same speed. Find the minimum speed of the neutron for which inelastic (completely or partially) collision may take place. The mass of neutron = mass of hydrogen = 1.67 × 10−27 kg.v
The earth revolves round the sun due to gravitational attraction. Suppose that the sun and the earth are point particles with their existing masses and that Bohr's quantization rule for angular momentum is valid in the case of gravitation. (a) Calculate the minimum radius the earth can have for its orbit. (b) What is the value of the principal quantum number n for the present radius? Mass of the earth = 6.0 × 10−24 kg. Mass of the sun = 2.0 × 1030 kg, earth-sun distance = 1.5 × 1011 m.
Obtain Bohr’s quantisation condition for angular momentum of electron orbiting in nth orbit in hydrogen atom on the basis of the wave picture of an electron using de Broglie hypothesis.
How are various lines of Lyman series formed? Explain on the basis of Bohr’s theory.
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.
Use Bohr's postulate to prove that the radius of nth orbit in a hydrogen atom is proportional to n2.
State Bohr's postulate to explain stable orbits in a hydrogen atom. Prove that the speed with which the electron revolves in nth orbit is proportional to `(1/"n")`.
An electron in H-atom makes a transition from n = 3 to n = 1. The recoil momentum of the H-atom will be ______.
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 atomic model of hydrogen, let K. P and E are the kinetic energy, potential energy and total energy of the electron respectively. Choose the correct option when the electron undergoes transitions to a higher level:
If 13.6 eV energy is required to ionize the hydrogen atom, then the energy required to remove an electron from n = 2 is ______.
According to Bohr's theory, the radius of the nth Bohr orbit of a hydrogen like atom of atomic number Z is proportional to ______.
State three postulates of Bohr's theory of hydrogen atom.
The energy of an electron in the nth orbit of the hydrogen atom is En = -13.6/n2eV. The negative sign of energy indicates that ______.
The radius of hydrogen atom in the ground state is 0.53 Å. The radius of Li2+ ion (atomic number = 3) in a similar state is ______.
