Question

Based on equation $E=-2.178\times {10}^{-18}J\left(\frac{Z^2}{n^2}\right),$certain conclusions are written. Which of them is/are correct?

• A. Larger the value of n, the larger is the orbit radius
  
• B. This equation can be used to calculate the change in energy when the electron changes orbit
• C. For n = 1, the electron has a more negative energy than it does for n = 6, which mean that the electron is more loosely bound in the smallest allowed orbit
• D. The negative sign in equation means that the energy or electron bound to the nucleus is lower than it would be if the electrons were at the infinite distance from the nucleus.

Answer 1

Answer: (A), (B), (D)

The correct options are
A Larger the value of n, the larger is the orbit radius

B This equation can be used to calculate the change in energy when the electron changes orbit
D The negative sign in equation means that the energy or electron bound to the nucleus is lower than it would be if the electrons were at the infinite distance from the nucleus.

(a) Larger the value of n, larger is the atomic radius as r is proportional to $n^2$ as per Bohr's model. According to the given equaiton E is inversely proportional to $n^2,$ as n increases radius increases.

(b) This equation can be used to calculate the change in energy as electron changes the orbit.

(c) Energy of an electron at infinite distance from the nucleus is zero. As an electron approaches the nucleus, the attractive force on electron increases and hence the energy of electron decreases and thus becomes negative. Thus as the value of n decreases, i.e. lower the orbit is, more negative is the energy of the electron in it.

(d) The negative sign in equation means that the energy or electron bound to the nucleus is lower than it would be if the electrons were at the infinite distance from the nucleus.