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Chapter 18: Problem 2481

If \(13.6 \mathrm{eV}\) energy is required to ionise the hydrogen atom the energy required to remove the electron form \(n=2\) state is (A) Zero (B) \(10.2 \mathrm{eV}\) (C) \(6.8 \mathrm{eV}\) (D) \(3.4 \mathrm{eV}\)

Short Answer

Expert verified
The energy required to remove the electron from the n=2 state is \(10.2 \mathrm{eV}\).

Step by step solution

01

Calculate energy of n=2 state for hydrogen atom

We use the energy level formula for hydrogen atom: \[E_n = -\dfrac{13.6 \, \text{eV}}{n^2}\] Now substituting n=2 \[E_2 = -\dfrac{13.6 \, \text{eV}}{(2)^2} = -\dfrac{13.6 \, \text{eV}}{4} = -3.4\, \text{eV}\]
02

Calculate energy difference between n=1 and n=2 states

Since, the energy required to ionize the hydrogen atom (remove electron from n=1 state) is 13.6 eV, the energy of the ground state (n=1) is: \[E_1 = -13.6\, \text{eV}\] Now to find the energy required to remove the electron from the n=2 state, we calculate the energy difference between n=1 and n=2 states: \[\Delta E = E_2 - E_1 = (-3.4\, \text{eV}) - (-13.6\, \text{eV}) = 10.2\, \text{eV}\] So, the energy required to remove the electron from the n=2 state is 10.2 eV. The correct answer is (B) \(10.2 \mathrm{eV}\).

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Most popular questions from this chapter

If the binding energy of electron in a hydrogen atom is \(13.6 \mathrm{eV}\), the energy required to remove the electron form the first state of \(\mathrm{Li}^{2+}\) is. (A) \(13.6 \mathrm{eV}\) (B) \(30.6 \mathrm{eV}\) (C) \(122.4 \mathrm{eV}\) (D) \(3.4 \mathrm{eV}\)

A radio-active nucleus \({ }^{\mathrm{A}} \mathrm{Z} \mathrm{X}\) emits $3 \alpha$ -particles and 2 Positrons. the ratio of number of neutron to that of Protons in the final nucleus will be (A) \([(\mathrm{A}-\mathrm{Z}-8) /(\mathrm{Z}-8)]\) (B) \([(\mathrm{A}-\mathrm{Z}-12) /(\mathrm{Z}-4)]\) (C) \([(\mathrm{A}-\mathrm{Z}-4) /(\mathrm{Z}-8)]\) (D) \([(A-Z-4) /(Z-2)]\)

when \(u-238\) nucleus originally at rest decay by emitting an \(\alpha\) -particle having a speed u the recoil speed of the residual nucleus is. (A) \([(4 \mathrm{u}) /(238)]\) (B) \([(-4 \mathrm{u}) /(238)]\) (C) \([(4 \mathrm{u}) /(234)]\) (D) \([(-4 \mathrm{u}) /(234)]\)

\(\mathrm{A}\) and \(\mathrm{B}\) are two radioactive substance whose half lives are 1 and 2 years respectively. Initially \(10 \mathrm{~g}\) of \(\mathrm{A}\) and \(1 \mathrm{~g}\) of \(\mathrm{B}\) is taken. The time after which they will have same quantity remaining is (A) \(3.6\) years (B) 7 years (C) \(6.6\) years (D) 5 years

excited hydrogen atom emits a Photon of wave length \(\lambda\) in returning to the ground state The quantum number \(\mathrm{n}\) of excited state is given by (A) \(\sqrt{[}(\lambda . \mathrm{R}-1) /(\lambda \mathrm{R})]\) (B) \(\sqrt{[}(\lambda \mathrm{R}) /(\lambda \mathrm{R}-1)]\) (C) \(\sqrt{[\lambda R}(\lambda \mathrm{R}-1)]\) (D) \(\lambda \mathrm{R}(\mathrm{R}-1)\)
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