Question

Sol. [Key Concept: Derive each from base quantities: $\lbrack h\rbrack = \lbrack E\rbrack/\lbrack\nu\rbrack$, $\lbrack V_{0}\rbrack = \lbrack E\rbrack/\lbrack q\rbrack$, $\lbrack\varphi\rbrack =$ energy, $\lbrack\nu_{0}\rbrack = T^{- 1}$; then match.]

(i) $\lbrack h\rbrack = \frac{\lbrack E\rbrack}{\lbrack v\rbrack} = \frac{{ML}^{2}{\text{ }T}^{- 2}}{{\text{ }T}^{- 1}} = {ML}^{2}{\text{ }T}^{- 1}$

(ii) Stopping potential : $E = q \cdot V_{0}$

$$\left\lbrack V_{0} \right\rbrack = \left\lbrack v_{0} \right\rbrack = \frac{\lbrack E\rbrack}{\lbrack q\rbrack} = \frac{{ML}^{2}{\text{ }T}^{- 2}}{AT} = {ML}^{2}{\text{ }T}^{- 3}{\text{ }A}^{- 1}$$

(iii) Work function $(\phi) \rightarrow$ Energy form

$$\lbrack\phi\rbrack = {ML}^{2}{\text{ }T}^{- 2}$$

(iv) Threshold freq. $\left\lbrack v_{0} \right\rbrack = T^{- 1}$