Question

Electron in Li+2 ion is present in orbit ‘x’ that has same total energy as that of electron in 1st excited state of H-atom. Identify the false statement regarding given information.


Velocity of electron in orbit ‘x’ is 1.09 × 106 m/s


Radius of orbit ‘x’ is 6.348 Å


Potential energy of electron in orbit ‘x’ is –3.4 eV


Kinetic energy of electron in (x – 1)th orbit is 4.896 eV

Answer 1

Electron in L²⁺ ion is present in orbit 'x' that has same total energy as that of electron in 1st excited state of H - atom.

To check false statement :

A. velocity of electron in orbit x is 1.09 × 10⁶ m/s

B. radius of orbit x is 6.348 A°

C. potential energy of electron in orbit x is -3.4 eV

D. kinetic energy of electron in (x - 1)th orbit is 4.896 eV

solution : total energy of an electron in x orbit is given by, T.E = -13.6 × Z²/x²

here Z = 3 ⇒T.E = -13.6 × 9/x² .........(1)

total energy of electron in 1st excited state of H - atom, T.E = -13.6 × (1)²/2² .........(2)

from equations (1) and (2) we get,

-13.6 × 1/2² = -13.6 × 9/x²

⇒x = 6

now let's check the statements.

velocity of electron in nth orbit is given by, v = 2.18 × 10⁶ Z/n

here Z = 3, n = 6

so, velocity of electron in xth orbit , v = 2.18 × 10⁶ × 3/6 = 1.09 × 10⁶ m/s

so option (A) is correct statement.

radius of nth orbit, r = 0.529 × n²/Z A°

here n = x = 6 and Z = 3

so, r = 0.529 × 6²/3 = 0.529 × 12 = 6.348 A°

option (B) is also correct statement.

potential energy = -27.2 × Z²/n² eV

= -27.2 × 3²/6²

= -27.2/4 = -6.8 eV

so option (C) is incorrect statement.

kinetic energy of electron in (x - 1)th orbit = 13.6 × 3²/5²

= 13.6 × 9/25

= 4.896 eV

option (D) is correct statement.

Therefore option (C) is a false statement.

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