## Question

####

A hydrogen atom rises from its *n* = 1 state to the *n* = 4 state by absorbing energy. If the potential energy of the atom in *n* = 1 state be –13.6 eV, thencalculate : potential energy in *n* = 4 state.

### Solution

Correct option is
–0.85 *eV*

The energy of the *n*th level of hydrogen atom is given by

Where *R* is Rydberg’s constant, *h* is Planck’s constant and *c* is speed of light. Thus, the energy of the lowest level (*n* = 1) is given by

.

The energy of the fourth-level (*n* = 4) is

.

Here *E*_{1} = –13.6 eV. So, energy in the state *n* = 4 is

#### SIMILAR QUESTIONS

Q1

In a head-on collision between an -particle and gold (*Z* = 79) nucleus, the closest distance of approach is 41.3 fermi. Calculate the energy of the -particle. (1 fermi = 10^{–15 }m)

Q2

Write down the expression for the radii of orbits of hydrogen atom. Calculate the radius of the smallest orbit.

Q3

In Bohr’s model of hydrogen atom, the radius of the first electron orbit is 0.53 Å. What will be the radius of the third orbit? What of the first orbit of singly-ionised helium atom?

Q4

Which energy state of the triply ionized beryllium (Be^{+++}) has the same orbital radius as that of the ground state of hydrogen? Compare the energies of the two states.

Q5

Calculate the speed of an electron revolving in the first orbit around the nucleus of a hydrogen atom in order that in order that it may not be pulled into the nucleus by electrostatic attraction.

Q6

Determine the speed of electron in the *n* = 3 orbit of He^{+}. Is the non-relativistic approximation valid? Datas as above.

Q7

The total energy (potential + kinetic) of an electron in the ground state of Bohr model of hydrogen atom is –13.6 eV. Obtain the values of the potential energy *U* and kinetic energy *K* in eV. Include –ve or +ve sign as required.

Q8

A muonic hydrogen atom is a bound state of a negatively-charged muon of mass 207*m*_{e} and a proton and the muon orbits around the proton. Obtain the radius of its first Bohr orbit.

Q9

The energy of an electron in an excited hydrogen atom is –3.4 eV. Calculate the angular momentum of the electron according to Bohr’s theory. Planck’s constant .

Q10

The ionization energy of the hydrogen atom is given to be 13.6 eV. A photon falls on a hydrogen atom which is initially in the ground state and excites it to the *n* = 4 state. Calculate the wavelength of the photon.