An α particle and a carbon 12 atom has same kinetic energy K. The ratio of their de-Broglie wavelength (λa: λC 12) is :

Question

An α particle and a carbon 12 atom has same kinetic energy K. The ratio of their de-Broglie wavelength (λa: λC 12) is : (A) 1: √3 (B) √3: 1 (C) 3: 1 (D) 2: √3

Tardigrade Admin · Accepted Answer

k=(P2/2 m) ⇒ P α √m Now λ=(h/p) So, λ α (1/p) ⇒ λ α (1/√m) (λα/λC 12)=(√3/1)

Q. An $α$ particle and a carbon $12$ atom has same kinetic energy $K$ . The ratio of their de-Broglie wavelength $(λ_{a} : λ_{C 12})$ is :

$1 : 3$

$3 : 1$

$3 : 1$

$2 : 3$

$k = \frac{P ^{2}}{2 m} \Rightarrow P α m$
Now $λ = \frac{h}{p}$
So, $λ α \frac{1}{p} \Rightarrow λ α \frac{1}{m}$
$\frac{λ _{α}}{λ _{C 12}} = \frac{3}{1}$

Q. An α particle and a carbon 12 atom has same kinetic energy K. The ratio of their de-Broglie wavelength (λa​:λC12​) is :

1:3​

3​:1

3:1

2:3​

k=2mP2​⇒Pαm​ Now λ=ph​ So, λαp1​⇒λαm​1​ λC12​λα​​=13​​

Q. An $α$ particle and a carbon $12$ atom has same kinetic energy $K$ . The ratio of their de-Broglie wavelength $(λ_{a} : λ_{C 12})$ is :

$1 : 3$

$3 : 1$

$3 : 1$

$2 : 3$

$k = \frac{P ^{2}}{2 m} \Rightarrow P α m$
Now $λ = \frac{h}{p}$
So, $λ α \frac{1}{p} \Rightarrow λ α \frac{1}{m}$
$\frac{λ _{α}}{λ _{C 12}} = \frac{3}{1}$