P = mv = h/λ

λ = h/mv

2πR = n λ = n h/mv

v = n h / 2πRm

Ke^2/R^2 = mv^2/R

mv^2 = Ke^2/R

v^2 = Ke^2/mR


v^2 = (n h / 2πRm)^2 = Ke^2/mR

-> n^2 h^2 / 4π^2 Rm = Ke^2

-> R = n^2 h^2 / 4π^2 m Ke^2


U = 운동E + 전기E

= 1/2mv^2 - Ke^2/R

= Ke^2/2R - Ke^2/R = -Ke^2/2R


R 대입

= -Ke^2 / 2 (n^2 h^2 / 4π^2 m Ke^2)

= -Ke^2 4π^2 m Ke^2 / 2 h^2 n^2

= -Ke^2 2π^2 m Ke^2 / h^2 n^2


ΔE = En - En' = hν = hc/λ


hc/λ = -(Ke^2 2π^2 m Ke^2 / h^2) (1/n^2 - 1/n'^2)

hc/λ = (Ke^2 2π^2 m Ke^2 / h^2) (1/n'^2 - 1/n^2)

1/λ = (Ke^2 2π^2 m Ke^2 / ch^3) (1/n'^2 - 1/n^2)


1/λ = Ｒ (1/n'^2 - 1/n^2) (n'<n)



여까지...... 이해 끝...