Question

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. 

Solution

Correct option is

4

The radius of the nth orbit of hydrogen-like atoms is given by 

           .  

  

where  is a constant. For the ground state (n = 1) of hydrogen atom (Z = 1), we have  

           r = k

Let n be the energy state of Be+++(Z = 4) for which the orbital radius is k(same as of hydrogen in ground state). Putting r = k and Z = 4 in eq. (i), we get 

          

.     

The energy of electron in the nth state of hydrogen-like atoms is given by       

           

.      

For   Be+++Z = 4, and n = 2; for HZ = 1 and n = 1.   

.

SIMILAR QUESTIONS

Q1

An -particle with kinetic energy 10 MeV is heading towards a stationary point-nucleus of atomic number Z = 50. Calculate the distance of closest approach.

   

Q2

 

An -particle with kinetic energy 10 MeV is heading towards a stationary point-nucleus of atomic number Z = 50. Calculate the distance of closest approach.

   

Q3

What is the distance of closest approach when a 5.0 MeV proton approaches a gold nucleus (Z = 79)? Given, 

    

.

Q4

An -particle after passing through a potential difference of  falls on a silver foil. The atomic number of silver is 47. Calculate the kinetic energy of the -particle at the time of falling on the foil. 

Q5

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 .

Q6

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.

Q7

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) 

Q8

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

  

 

Q9

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?

Q10

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.