Question

For Bohr’s atomic model of hydrogen and hydrogen like atoms, answer the following questions based on the columns below. Symbols have their usual meanings and, ‘n’ is principal quantum number, z is atomic number of atom.

$\begin{array}{cccccc}& Column1& & Column2& & Column3\\ & \left(Physicalquanties\right)& & \left(Forhydrogen\right)& & \left(Forhydrogenlikeatom\right)\\ \left(I\right)& Energyof{e}^{-}\left(E\right)is& \left(i\right)& n^3& \left(P\right)& \frac{z^2}{n^2}\\ & proportionalto& & & & \\ \left(II\right)& Velocityof{e}^{-}is& \left(ii\right)& n& \left(Q\right)& \frac{n}{z}\\ & proportionalto& & & & \\ \left(III\right)& Timeperiodofrevolution& \left(iii\right)& \frac{1}{n^2}& \left(R\right)& n\\ & proportionalto& & & & \\ \left(IV\right)& Angularmomentumis& \left(iv\right)& \frac{1}{n}& \left(s\right)& \frac{n^3}{z^2}\\ & proportionalto& & & & \end{array}$

Which option correctly matches with velocity of electron?

• A. (II), (iii), (S)
• B. (II), (i), (S)
• C. (II), (iv), (Q)

Answer 1

The correct option is C

(II), (iv), (Q)

Direct formula based:$E\propto \frac{z^2}{n^2};V\propto \frac{z}{n};T\propto \frac{n^3}{z^2};$