If the velocity of the electron in Bohr's first orbit is 2.19 × 10⁶ ms⁻¹, calculate the de Broglie wavelength associated with it.

The de Broglie wavelength (λ) is given by the equation:
λ = h/mv
where:
h = Planck's constant (6.626 × 10⁻³⁴ Js)
m = mass of the electron (9.11 × 10⁻³¹ kg)
v = velocity of the electron (2.19 × 10⁶ ms⁻¹)
Substituting the values:
λ = (6.626 × 10⁻³⁴ Js) / (9.11 × 10⁻³¹ kg × 2.19 × 10⁶ ms⁻¹)
λ = 3.32 × 10⁻¹⁰ m
Converting to picometers (pm):
λ = 3.32 × 10⁻¹⁰ m × (10¹² pm/1 m) = 332 pm