Question

The ratio of the radii of two orbits of an unielectronic atom is 1 : 4. The ratio of the total energy in these orbit will be x : 1. The value of x is

Answer 1

Answer:

x=2

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Explanation:

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Answer 2

The ratio of the total energy in these orbit will be 4 : 1.

Explanation:

• The relation between radius and orbital for unielectron atom is given by -

                r ∝ n² ; where r is radius, n is the orbit.

            = n² = r

• Given ratio of radii of two orbits is 1:4
• Let r1² be 1 and r2² be 4.

• The relation between Energy and orbital for unielectron atom is given by-

                E ∝ -Z²/ n²

                En = -13.6 x Z²/ n² ; where En is the Energy of the nth orbital

• Given ratio of the energy of two orbits is x:1

•   Let E1 be x and E2 be 1.

• To calculate the value of x

          Using the above two relations, we get:

                E2/ E1 = (-13.6 Z²/ r2²) / (-13.6 Z²/ r1²)

                E2/ E1 = r1²/r2²

                Substituting the values,

               1 / x = 1/4

                    x  = 4

The ratio of the total energy in these orbit will be x : 1 = 4:1.