Answer:
8.01 (10^-10) m
Explanation:
use the Particle in a box equation
E = (n^2) (h^2) / (8 m (L^2))
and energy of a particle as its wavelength equation
h c / lamda = E
combine the equations to get
h c / lamda = (n^2) (h^2) / (8 m (L^2))
get L alone
L^2 = (2^2 - 1^2) h lamda / 8 m c
the longest wavelength is produced by a jump from the first excited state to the ground so
n = 2 to n = 1
so
L^2 = (n1^2 - n2^2) h lamda / (8 m c)
h = 6.6(10^-34) J*s
c = 3(10^8) m/s
m = 9(10^-31) kg
lamda = 700(10^-9) m
n1 =2
n2=1
