Answer :
For a particle confined to a one-dimensional box, the momentum can be determined using the de Broglie wavelength. The de Broglie wavelength (λ) of a particle is given by the equation λ = h / p, where h is the Planck constant and p is the momentum of the particle.for the particle in the n = 1 state, its momentum is 3.32 × 10⁻²⁴ kg·m/s.
Since we are considering the n = 1 state, it corresponds to the ground state or the lowest energy state of the particle in the box. In the ground state, the particle exhibits a half-wavelength within the length of the box. Therefore, the de Broglie wavelength (λ) is equal to twice the length of the box (2L).
Given that the length of the box is 1.00 × 10⁻¹⁰ m, we can calculate the de Broglie wavelength:
λ = 2L = 2 * (1.00 × 10⁻¹⁰ m) = 2.00 × 10⁻¹⁰ m
Now, we can rearrange the de Broglie wavelength equation to solve for momentum:
p = h / λ
Substituting the values:
p = (6.63 × 10⁻³⁴ J·s) / (2.00 × 10⁻¹⁰ m)
Calculating the momentum:
p = 3.32 × 10⁻²⁴ kg·m/s
To learn more about de Broglie wavelength , Click here: brainly.com/question/17295250
#SPJ11
