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: 2×10⁻¹³ m

Step-by-step 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

Answer 2

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

We need to find the wavelength of the deutrons which are travelling with a velocity of
`1*10^6m/s`. we would use de-Broglie's formula which relates momentum of the particle with its wavelength.

`\lambda=(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* 1.67*10^(-27) kg=3.34*10^(-27) kg` (because of mass of proton =mass of neutron =
`1.67*10^(-27)kg`

`\Rightarrow \lambda=(6.626*10^(-34)J.s)/(3.34*10^(-27)kg*10^6m/s)=1.98*10^(-13)m`

Therefore, the wavelength of the deutrons travelling with the speed
`10^6 m/s` is
`1.98*10^(-13)m`