Experimentally it is found that 12 . 8 eV energy is required to separate a hydrogen atom into a proton and an electron. So the orbital radius of the electron in a hydrogen atom is 9 x × 10 - 10 m . The value of the x is: _____. ( 1 eV = 1 . 6 × 10 - 19 J , 1 4 π ε 0 = 9 × 10 9 Nm 2 C 2 and electronic charge = 1 . 6 × 10 - 19 C )

Step-by-step solution

The given data is q = 1 . 6 × 10 - 19   C 1 4 πε 0 = 9 × 10 9   N   m 2   C - 2 The formula for the value of energy in a hydrogen atom is given by E = q 2 8 π ε 0 r ⇒ E = q 2 2 ( 4 π ε 0 ) r ⇒ r = 9 × 10 9 × 1 . 6 × 10 - 19 12 . 8 × 2 ⇒ r = 9 16 × 10 - 10   m It is given that r = 9 x × 10 - 10   m ⇒ 9 16 × 10 - 10 = 9 x × 10 - 10   ⇒ x = 16