Match List I with List II List I List II A . Planck's constant (h) I . [ M ^ 1 L ^ 2 T ^ - 2 ] B . Stopping potential ( V _ s ) II . [ M ^ 1 L ^ 1 T ^ - 1 ] C . Work function (ϕ) III . [ M ^ 1 L ^ 2 T ^ - 1 ] D .

JEE Main 202324 JanuaryMorning Shift

JEE Main 2023 · 24 January · Morning Shift · Physics · Units and Dimensions

Match List I with List II List I List II A . Planck's constant (h)...

Match List I with List II

List I		List II
$A .</td> <td>Planck's constant \left(h\right)</td> <td>$ I .	\left[{M}^{1}{L}^{2}{T}^{- 2}\right] $</td> </tr> <tr> <td>$ B .	Stopping potential \left({V}_{s}\right)	$II .</td> <td>\left[{M}^{1}{L}^{1}{T}^{- 1}\right]$
$C .</td> <td>Work function \left(ϕ\right)</td> <td>$ III .	\left[{M}^{1}{L}^{2}{T}^{- 1}\right] $</td> </tr> <tr> <td>$ D .	Momentum \left(p\right)	$IV .</td> <td>\left[{M}^{1}{L}^{2}{T}^{- 3}{A}^{- 1}\right]$

B. $A - III, B - IV, C - I, D - II$

The dimension of momentum is,

$p = \left[{M}^{1}{L}^{1}{T}^{- 1}\right]$

From de Broglie equation,

$\dfrac{h}{p} = \lambda$

$[ h ] = [ p ] \left[\lambda\right] = \left[M{L}^{2}{T}^{- 1}\right]$

The stopping potential is related to maximum kinetic energy of emitted electron as

${V}_{s} = \dfrac{K{E}_\max}{e}$

$= \dfrac{\left[{ML}^{2}{T}^{- 2}\right]}{\left[AT\right]} = \left[{ML}^{2}{T}^{- 3}{A}^{- 1}\right]$

From Einstein's photoelectric equation, the work function $ϕ$ has dimensions of energy

\left[ϕ\right] = \left[{ML}^{2}{T}^{- 2}\right]$