Question

question 2
the wavelength (λ) and frequency (ν) of light are related through the equation: c = λ×ν
where:
c = speed of light (3.00×10⁸ m·s⁻¹)
λ = wavelength (m)
ν = frequency (s⁻¹)
using the following emission spectrum:
calculate the frequency for each of the 7 emission lines (1 nm = 1×10⁻⁹m):
a) violet (450 nm)
b) indigo (470 nm)
c) blue (490 nm)
d) green (520 nm)
e) yellow (620 nm)
f) orange (630 nm)
g) red (690 nm)

Explanation:

Step1: Rearrange the formula for frequency

Given $c = \lambda\times
u$, we can solve for $
u$ as $
u=\frac{c}{\lambda}$.

Step2: Convert wavelength to meters

For each wavelength value in nanometers, convert it to meters by multiplying by $10^{-9}$.

Step3: Calculate frequency for each line

a) Violet

$\lambda = 450\ nm=450\times 10^{-9}\ m$
$
u=\frac{c}{\lambda}=\frac{3.00\times 10^{8}\ m\cdot s^{-1}}{450\times 10^{-9}\ m}\approx6.67\times 10^{14}\ s^{-1}$

b) Indigo

$\lambda = 470\ nm = 470\times 10^{-9}\ m$
$
u=\frac{c}{\lambda}=\frac{3.00\times 10^{8}\ m\cdot s^{-1}}{470\times 10^{-9}\ m}\approx6.38\times 10^{14}\ s^{-1}$

c) Blue

$\lambda = 490\ nm=490\times 10^{-9}\ m$
$
u=\frac{c}{\lambda}=\frac{3.00\times 10^{8}\ m\cdot s^{-1}}{490\times 10^{-9}\ m}\approx6.12\times 10^{14}\ s^{-1}$

d) Green

$\lambda = 520\ nm = 520\times 10^{-9}\ m$
$
u=\frac{c}{\lambda}=\frac{3.00\times 10^{8}\ m\cdot s^{-1}}{520\times 10^{-9}\ m}\approx5.77\times 10^{14}\ s^{-1}$

e) Yellow

$\lambda = 620\ nm=620\times 10^{-9}\ m$
$
u=\frac{c}{\lambda}=\frac{3.00\times 10^{8}\ m\cdot s^{-1}}{620\times 10^{-9}\ m}\approx4.84\times 10^{14}\ s^{-1}$

f) Orange

$\lambda = 630\ nm=630\times 10^{-9}\ m$
$
u=\frac{c}{\lambda}=\frac{3.00\times 10^{8}\ m\cdot s^{-1}}{630\times 10^{-9}\ m}\approx4.76\times 10^{14}\ s^{-1}$

g) Red

$\lambda = 690\ nm=690\times 10^{-9}\ m$
$
u=\frac{c}{\lambda}=\frac{3.00\times 10^{8}\ m\cdot s^{-1}}{690\times 10^{-9}\ m}\approx4.35\times 10^{14}\ s^{-1}$

Answer:

a) $6.67\times 10^{14}\ s^{-1}$
b) $6.38\times 10^{14}\ s^{-1}$
c) $6.12\times 10^{14}\ s^{-1}$
d) $5.77\times 10^{14}\ s^{-1}$
e) $4.84\times 10^{14}\ s^{-1}$
f) $4.76\times 10^{14}\ s^{-1}$
g) $4.35\times 10^{14}\ s^{-1}$