Question

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.

 

 

Solution

Correct option is

The radius of first (n = 1) Bohr orbit of hydrogen atom (Z = 1) is given by 

       

            

          

The radius of the first orbit of muonic atom will be 

       

           

         

SIMILAR QUESTIONS

Q1

A beam of -particles of velocity  is scattered by a gold (Z = 79) foil. Find out the distance closest approach of the -particle to the gold nucleus. The value of charge/mass for -particle is .

Q2

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.

Q3

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) 

Q4

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

  

 

Q5

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?

Q6

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. 

Q7

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.

Q8

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

Q9

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.

Q10

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 .