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Chapter 18: Problem 2552

As the electron in Bohr is orbit of hydrogen atom Passes from state \(\mathrm{n}=2\) to \(\mathrm{n}=1\), the \(\mathrm{K} . \mathrm{E}\). and Potential energy changes as (A) Two fold, also two fold (B) four fold, two fold (C) four fold, also four fold (D) two fold, four fold

Short Answer

Expert verified
As the electron in the hydrogen atom transitions from n = 2 to n = 1, both the kinetic energy and potential energy change by a factor of 4. Therefore, the correct answer is (C) four fold, also four fold.

Step by step solution

01

1. Recall the formula for kinetic and potential energy in Bohr's model.

In Bohr's model, the kinetic energy (KE) and potential energy (PE) of an electron in the hydrogen atom, at a particular energy level n, are given by: KE = \(\frac{KZe^2}{2\cdot a_0\cdot n^2}\) and PE = \(\frac{-KZe^2}{a_0\cdot n^2}\) Here, K is Coulomb's constant, Z is the atomic number (Z = 1 for hydrogen), e is the elementary charge, and \(a_0\) is the Bohr's radius.
02

2. Calculate the ratio of kinetic energies and potential energies at the two principal quantum numbers n = 1 and n = 2.

We will find the ratio of the kinetic energy at n = 2 to the kinetic energy at n = 1, and similarly for the potential energy. \(\frac{KE_2}{KE_1}\) = \(\frac{\frac{KZe^2}{2\cdot a_0\cdot 4}}{\frac{KZe^2}{2\cdot a_0}}\) = \(\frac{1}{4}\) \(\frac{PE_2}{PE_1}\) = \(\frac{\frac{-KZe^2}{a_0 \cdot 4}}{\frac{-KZe^2}{a_0}}\) = \(\frac{1}{4}\)
03

3. Analyze the changes in kinetic and potential energy.

From the ratios calculated in step 2, we can see that as the electron transitions from n = 2 to n = 1, both the kinetic energy and potential energy change four-fold (reduced by a factor of 4). So, the correct answer is: (C) four fold, also four fold.

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Most popular questions from this chapter

The half life time of a radioactive elements of \(\mathrm{x}\) is the same as the mean life of another radioactive element \(\mathrm{y}\). Initially they have same number of atoms, then (A) \(\mathrm{y}\) will decay faster then \(\mathrm{x}\) (B) \(\mathrm{x}\) will decay faster then \(\mathrm{y}\) (C) \(\mathrm{x}\) and \(\mathrm{y}\) will decay at the same rate at all time (D) \(\mathrm{x}\) and \(\mathrm{y}\) will decay at the same rate initially.

\(\mathrm{A}\) 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

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