Question

the electromagnetic spectrum and electronic transitions
radiation wavelength
the energy associated with the electronic transition from n = 2 to n = 5 is the absorption of 4.57 x 10⁻¹⁹ j.
calculate the wavelength, in nm, of the radiation associated with this transition.
useful equations and constants:
$c = \lambda\
u$
$e = h\
u$
$c = 3.0 \times 10^8$ m/s
$h = 6.626 \times 10^{-34}$ j·s
avogadros number = $6.02 \times 10^{23}$ mol⁻¹
what is the wavelength, in nm, of the radiation associated with the spectral line?

1. nm

4.35 x 10⁻⁷ nm
6.90 x 10¹⁴ nm
435 nm

Explanation:

Step1: Relate E, c, λ

Combine $c = \lambda
u$ and $E = h
u$ to get $E = \frac{hc}{\lambda}$. Rearrange for $\lambda$:
$\lambda = \frac{hc}{E}$

Step2: Plug in known values

Substitute $h=6.626\times10^{-34}\ \text{J·s}$, $c=3.0\times10^8\ \text{m/s}$, $E=4.57\times10^{-19}\ \text{J}$:
$\lambda = \frac{(6.626\times10^{-34})\times(3.0\times10^8)}{4.57\times10^{-19}}$

Step3: Calculate wavelength in meters

Compute the value:
$\lambda = 4.35\times10^{-7}\ \text{m}$

Step4: Convert meters to nanometers

Use $1\ \text{m}=10^9\ \text{nm}$:
$\lambda = 4.35\times10^{-7}\times10^9 = 435\ \text{nm}$

Answer:

435 nm