Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
Obtain an expression for the radius of Bohr orbit for H-atom.
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, derive the expression for the total energy of the electron in the stationary states of the hydrogen atom ?
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.
Using Bohr’s postulates, derive the expression for the frequency of radiation emitted when electron in hydrogen atom undergoes transition from higher energy state (quantum number ni) to the lower state, (nf).
When electron in hydrogen atom jumps from energy state ni = 4 to nf = 3, 2, 1, identify the spectral series to which the emission lines belong.
The numerical value of ionization energy in eV equals the ionization potential in volts. Does the equality hold if these quantities are measured in some other units?
The numerical value of ionization energy in eV equals the ionization potential in volts. Does the equality hold if these quantities are measured in some other units?
According to Maxwell's theory of electrodynamics, an electron going in a circle should emit radiation of frequency equal to its frequency of revolution. What should be the wavelength of the radiation emitted by a hydrogen atom in ground state if this rule is followed?
According to Bohr, 'Angular momentum of an orbiting electron is quantized'. What is meant by this statement?
If l3 and l2 represent angular momenta of an orbiting electron in III and II Bohr orbits respectively, then l3: l2 is :
Which of the following is/are CORRECT according to Bohr's atomic theory?
(I) Energy is emitted when electron moves from a higher stationary state to a lower one.
(II) Orbits are arranged concentrically around the nucleus in an increasing order of energy.
(III) The energy of an electron in the orbit changes with time.
According to Bohr's model of hydrogen atom, an electron can revolve round a proton indefinitely, if its path is ______.
When an electric discharge is passed through hydrogen gas, the hydrogen molecules dissociate to produce excited hydrogen atoms. These excited atoms emit electromagnetic radiation of discrete frequencies which can be given by the general formula
`bar(v) = 109677 1/n_1^2 - 1/n_f^2`
What points of Bohr’s model of an atom can be used to arrive at this formula? Based on these points derive the above formula giving description of each step and each term.
Why was a change in the Bohr Model of atom required? Due to which important development (s), concept of movement of an electron in an orbit was replaced by, the concept of probability of finding electron in an orbital? What is the name given to the changed model of atom?
An ionised H-molecule consists of an electron and two protons. The protons are separated by a small distance of the order of angstrom. In the ground state ______.
- the electron would not move in circular orbits.
- the energy would be (2)4 times that of a H-atom.
- the electrons, orbit would go around the protons.
- the molecule will soon decay in a proton and a H-atom.
The inverse square law in electrostatics is |F| = `e^2/((4πε_0).r^2)` for the force between an electron and a proton. The `(1/r)` dependence of |F| can be understood in quantum theory as being due to the fact that the ‘particle’ of light (photon) is massless. If photons had a mass mp, force would be modified to |F| = `e^2/((4πε_0)r^2) [1/r^2 + λ/r]`, exp (– λr) where λ = mpc/h and h = `h/(2π)`. Estimate the change in the ground state energy of a H-atom if mp were 10-6 times the mass of an electron.
The electron in a hydrogen atom first jumps from the third excited state to the second excited state and subsequently to the first excited state. The ratio of the respective wavelengths, λ1/λ2, of the photons emitted in this process is ______.
What is the energy of an electron in stationary state corresponding to n = 2?
An electron in a hydrogen atom has an energy of -3.4 eV. The difference between its kinetic and potential energy is ______.
State three postulates of Bohr's theory of hydrogen atom.
