Question

The radius of a cadmium atom is approximately 0.16 nm. What is the magnitude of the ionization energy? (in joules)

Answer 1

Step 1: Using Bohr's radius equation, we know that:

r = (0.529*10^-10)*n^2/Z

Given that radius of cadmium atom is 0.16 nm, So

r = 0.16*10^-9 m = 1.6*10^-10 m

So,

1.6*10^-10 = 0.529*10^-10*(n^2/Z)

n^2/Z = 1.6/0.529

Step 2: Now magnitude of ionization energy of atoms is given by:

E = 13.6 eV*(Z^2/n^2)

1 eV = 1.6*10^-19 J

Z = atomic number of Cadmium = 48

So,

E = 13.6*1.6*10^-19*Z*(Z/n^2)

E = 13.6*1.6*10^-19*48*(0.529/1.6)

E = 3.45*10^-17 J = Magnitude of ionization energy

Let me know if you've any query.