Question

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 .  

Solution

Correct option is

In hydrogen atom, the energy of electron in the nth energy level is

         

Here   E­n = –3.4 eV. From this, we have    

             n = 2. 

According to Bohr’s theory, the angular momentum of the electron is 

           

SIMILAR QUESTIONS

Q1

What is the upper limit of the radius of the gold nuclues (Z = 79), if an -particle of energy 12.5 MeV is deflected back by the nucleus through 180o.

Q2

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) 

Q3

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

  

 

Q4

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?

Q5

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. 

Q6

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.

Q7

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

Q8

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.

Q9

A muonic hydrogen atom is a bound state of a negatively-charged muon  of mass 207me and a proton and the muon orbits around the proton. Obtain the radius of its first Bohr orbit.

 

 

Q10

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.