Question

In order for a thermonuclear fusion reaction of two deuterons (21h+) to occur, the deuterons must collide each with a velocity of about 1×106m/s. what is the wavelength?

Answer 1

Answer: 1.98\times10^{-13}m[/tex]

We need to find the wavelength of the deutrons which are travelling with a velocity of $1\times10^6m/s$.  we would use de-Broglie's formula which relates momentum of the particle with its wavelength.

$\lambda=\frac{h}{mv}$

where, h = Planck's constant

m is the mass

v is the velocity

and $\lambda$ is the wavelength.

Deutron has 1 neutron and 1 proton.

Mass of deutron is $2\times 1.67\times10^{-27} kg=3.34\times10^{-27} kg$ (because of mass of proton =mass of neutron = $1.67\times10^{-27}kg$

$\Rightarrow \lambda=\frac{6.626\times10^{-34}J.s}{3.34\times10^{-27}kg\times10^6m/s}=1.98\times10^{-13}m$

Therefore, the wavelength of the deutrons travelling with the speed $10^6 m/s$ is $1.98\times10^{-13}m$

Answer 2

Answer: 2×10⁻¹³ m

Explanation:

1) Data:

• particle: deuteron nucleus, ²₁H
• λ = ?
• v = 1×10⁶m/s

2) Formula

• De Broglie's equation:  (λ):

           λ = h/(m×v)

           Where h is the Planck constant, h = 6.626×10⁻³⁴ J s

• mass of a nucleus = mass of protons + mass of neutrons

3) Solution:

a) mass of ²₁H

• ²₁H ⇒ 1 neutron and 1 proton ⇒
• m = 1.675×10⁻²⁷kg + 1.673×10⁻²⁷kg = 3.348×10⁻²⁷ kg

b) wavelength

• λ = h/(m×v) = 6.626×10⁻³⁴ / [(3.348×10⁻²⁷)×(1×10⁶)] = 1.98×10⁻¹³ m
• Round to one significant figure: 2×10⁻¹³ m