Advertisements
Advertisements
Question
Find the maximum Coulomb force that can act on the electron due to the nucleus in a hydrogen atom.
Advertisements
Solution
Charge on the electron, q1 = `1.6 xx 10^-19 C`
Charge on the nucleus, q2 = `1.6 xx 10^-19 C`
Let r be the distance between the nucleus and the electron.
Coulomb force (F) is given by
`F = (q_1q_2)/(4 pi∈_0r^2) ........(1)`
Here , q1 = q2 = q = 1.6`xx 10^-19C`
000 Smallest distance between the nucleus and the first orbit, r = 0.53 `r = 0.53xx10^-10m `
`K= 1/(4piepsilon_0) = 9 xx 10^9Nm^2C^-2`
Substituting the respective values in (1), we get
`F =((9xx10^9)xx(1.6xx10^-19)xx(1.6xx10^-19))/(0.53xx10^-10)^2`
= `(1.6xx1.6xx9xx10^-9)/(0.53) = 82.02 xx 10^-9`
= `8.2xx10^-8 N`
APPEARS IN
RELATED QUESTIONS
If Bohr’s quantisation postulate (angular momentum = nh/2π) is a basic law of nature, it should be equally valid for the case of planetary motion also. Why then do we never speak of quantisation of orbits of planets around the sun?
When white radiation is passed through a sample of hydrogen gas at room temperature, absorption lines are observed in Lyman series only. Explain.
The minimum orbital angular momentum of the electron in a hydrogen atom is
A hydrogen atom in ground state absorbs 10.2 eV of energy. The orbital angular momentum of the electron is increased by
Calculate the smallest wavelength of radiation that may be emitted by (a) hydrogen, (b) He+ and (c) Li++.
Find the radius and energy of a He+ ion in the states (a) n = 1, (b) n = 4 and (c) n = 10.
Whenever a photon is emitted by hydrogen in Balmer series, it is followed by another photon in Lyman series. What wavelength does this latter photon correspond to?
Find the maximum angular speed of the electron of a hydrogen atom in a stationary orbit.
Suppose, in certain conditions only those transitions are allowed to hydrogen atoms in which the principal quantum number n changes by 2. (a) Find the smallest wavelength emitted by hydrogen. (b) List the wavelength emitted by hydrogen in the visible range (380 nm to 780 nm).
Average lifetime of a hydrogen atom excited to n = 2 state is 10−8 s. Find the number of revolutions made by the electron on the average before it jumps to the ground state.
Show that the ratio of the magnetic dipole moment to the angular momentum (l = mvr) is a universal constant for hydrogen-like atoms and ions. Find its value.
A hydrogen atom moving at speed υ collides with another hydrogen atom kept at rest. Find the minimum value of υ for which one of the atoms may get ionized.
The mass of a hydrogen atom = 1.67 × 10−27 kg.
When a photon is emitted from an atom, the atom recoils. The kinetic energy of recoil and the energy of the photon come from the difference in energies between the states involved in the transition. Suppose, a hydrogen atom changes its state from n = 3 to n = 2. Calculate the fractional change in the wavelength of light emitted, due to the recoil.
In a hydrogen atom the electron moves in an orbit of radius 0.5 A° making 10 revolutions per second, the magnetic moment associated with the orbital motion of the electron will be ______.
Let En = `(-1)/(8ε_0^2) (me^4)/(n^2h^2)` be the energy of the nth level of H-atom. If all the H-atoms are in the ground state and radiation of frequency (E2 - E1)/h falls on it ______.
- it will not be absorbed at all.
- some of atoms will move to the first excited state.
- all atoms will be excited to the n = 2 state.
- no atoms will make a transition to the n = 3 state.
In the Auger process an atom makes a transition to a lower state without emitting a photon. The excess energy is transferred to an outer electron which may be ejected by the atom. (This is called an Auger electron). Assuming the nucleus to be massive, calculate the kinetic energy of an n = 4 Auger electron emitted by Chromium by absorbing the energy from a n = 2 to n = 1 transition.
