C=q/ Δφ,
C=εε₀A/d,
q/ Δφ = εε₀A/d,
q= εε₀A Δφ /d,
where ε =4.1, ε₀=8.85 •10⁻¹² F/m,
A=4.4•10⁻⁹m²,
d=1.64.4•10⁻⁸ m,
N=q/e=q/1.6•10⁻¹⁹ = …
C=εε₀A/d,
q/ Δφ = εε₀A/d,
q= εε₀A Δφ /d,
where ε =4.1, ε₀=8.85 •10⁻¹² F/m,
A=4.4•10⁻⁹m²,
d=1.64.4•10⁻⁸ m,
N=q/e=q/1.6•10⁻¹⁹ = …
C = (ε₀ * ε * A) / d
Where:
C = Capacitance
ε₀ = Permittivity of free space (8.85 x 10^-12 F/m)
ε = Dielectric constant
A = Surface area of the membrane
d = Thickness of the membrane
(a) To find the charge on the outer surface, we can use the formula for capacitance:
C = Q / V
Where:
Q = Charge on the outer surface
V = Potential difference between the outer and inner surfaces
Rearranging the formula, we get:
Q = C * V
Substituting the given values:
C = (ε₀ * ε * A) / d = (8.85 x 10^-12 F/m * 4.1 * 4.4 x 10^-9 m^2) / (1.6 x 10^-8 m)
V = 66.4 mV = 66.4 x 10^-3 V
Calculating the charge:
Q = (8.85 x 10^-12 F/m * 4.1 * 4.4 x 10^-9 m^2) / (1.6 x 10^-8 m) * (66.4 x 10^-3 V)
(b) To find the number of K+ ions on the outer surface, we need to know the charge of each K+ ion. Given that the charge of a K+ ion is +e, we can find the number of ions:
Number of ions = Q / e
Substituting the values:
Number of ions = Q / +e
Now you can calculate both the charge on the outer surface and the number of K+ ions present on the outer surface using the given information and the equations provided above.