Question

The ratio of wavelengths of proton and deuteron accelerated by potential V_p and V_d is 1 : `sqrt2`. Then, the ratio of V_p to V_d will be ______.

Options

• 1 : 1

• `sqrt2` : 1

• 3 : 1

• 4 : 1

Answer 1

The ratio of wavelengths of proton and deuteron accelerated by potential V_p and V_d is 1 : `sqrt2`. Then, the ratio of V_p to V_d will be 4 : 1.

Explanation:

The kinetic energy gained by a charged particle accelerated by a potential V is denoted by the symbol qV.

KE = qV

⇒ `"p"^2/(2"m")` = qV  ⇒ p = `sqrt(2"mqV")`

p = `"h"/lambda` ⇒ λ = `"h"/(sqrt(2"mqV"))`

now `lambda_"p"/lambda_"d"=sqrt(("m"_"d""V"_"d")/("m"_"p""V"_"p"))`

⇒ `1/sqrt2 = sqrt((2"V"_"d")/("V"_"p"))` 

⇒ `"V"_"p"/"V"_"d"`

= 4