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# In which of the following cases the heavier of the two particles has a smaller de-Broglie wavelength? The two particles

$\begin {array} {1 1} (1)\;move\: with \: same \: speed & \quad (2)\;move \: with\: same \: linear \: momentum \\ (3)\;move \: with \: same\: KE & \quad (4)\;have \: the\: same\: change\: of\: potential \: energy\: in\: a \: conservative\: field \end {array}$

$\begin {array} {1 1} (a)\;1,2 \: and \: 3 & \quad (b)\;2 \: and \: 4 \\ (c)\;2\: and \: 3 & \quad (d)\;1,3 \: and \: 4 \end {array}$

Ans : (d)
1.$\lambda = \large\frac{h}{mv}\:\: \: \: \; So, \lambda \sim \large\frac{1}{m}$
2. $\lambda = \large\frac{h}{p}\: \: \: \: \:\: \: So, \lambda$ doesn’t depend on $m$
3. $\lambda = \large\frac{h}{ \sqrt {2mE}}\: \: \: \: \: So, \lambda \sim \large\frac{1}{ \sqrt m}$
4. $\lambda = \large\frac{h}{ \sqrt {2meV}}\: So, \lambda sim \large\frac{1}{ \sqrt m}$

edited Mar 13, 2014