Answer:
a) wavelength = 656.3 nm
b) the value of Rydberg's constant for this measurement is 1.097 × 10⁷ m⁻¹
Explanation:
Given that;
angle of diffraction Θₓ = 22.78°
incident angle Θ₁ = 0
slit separation d = 5900 lines per cm = 1/5900 cm = 10⁻²/5900 m = 0.01/5900 m
order of diffraction n = 1
wavelength λ = ?
to find the wavelength, we use the expression
λ = d (sinΘ₁ + sinΘₓ) / n
To find the wavelength λ;
λ = 0.01/5900 × (sin0 + sin22.78° )
λ = 6.5626 × 10⁻⁷ m
λ = 656.3 x 10⁻⁹ m
∴ λ = 656.3 nm
b)
According Balnur's series spectral lines; n₁ = 3, n₂ = 2 and
λ = R [ 1/n₂² - 1/n₁²]
where R is Rydberg's constant
from λ = R [ 1/n₂² - 1/n₁²]
R = 1/λ [n₂²n₁² / n₁² - n₂²]
R = 10⁹/ 656.3 [ 9 × 4 / 9 - 4 ]
R = 1.097 × 10⁷ m⁻¹
Therefore the value of Rydberg's constant for this measurement is 1.097 × 10⁷ m⁻¹
Answer:
a) 1.082 × 10⁻¹⁹C ( e = 1.6 × 10⁻¹⁹C)
b) 3.466 × 10¹¹ N/C
Explanation:
a)
p(r) = -A exp ( - 2r/a₀)
Q = ₀∫^∞ ₀∫^π ₀∫^2xπ p(r)dV = -A ₀∫^∞ ₀∫^π ₀∫^2π exp ( - 2r/a₀)r² sinθdrdθd∅
Q = -4πA ₀∫^∞ exp ( - 2r/a₀)r²dr = -e
now using integration by parts;
A = e / πa₀³
p(r) = - (e / πa₀³) exp (-2r/a₀)
Now Net charge inside a sphere of radius a₀ i.e Qnet is;
= e - (e / πa₀³) ₀∫^a₀ ₀∫^π ₀∫^2π r² exp (-2r/a₀)dr
= e - e + 5e exp (-2) = 1.082 × 10⁻¹⁹C ( e = 1.6 × 10⁻¹⁹C)
b)
Using Gauss's law,
E × 4πa₀ ² = Qnet / ∈₀
E = 4πa₀ ² × Qnet × 1/a₀²
E = 3.466 × 10¹¹ N/C
The light must be either very dim or else non-existent.
We can't see the light wave or the label.