Yellow colors in fireworks are die to the 589 nm radiation of sodium ions.
a.) How much energy is given off by one photon of sodium?
E = hc/wavelength
The 589 nm must be changed to m.
To calculate the energy of one photon, you can use the equation:
Energy (E) = Planck's constant (h) * frequency (ν)
The frequency (ν) can be calculated using the speed of light (c) and the wavelength (λ):
ν = c / λ
Given that the wavelength (λ) of sodium's 589 nm radiation, we can convert it to meters:
λ = 589 nm = 589 * 10^(-9) m
The speed of light (c) is approximately 3.00 x 10^8 meters per second.
So, let's calculate the frequency (ν):
ν = c / λ
= (3.00 x 10^8 m/s) / (589 * 10^(-9) m)
≈ 5.09 x 10^14 Hz
Now, we can use the value of frequency (ν) to find the energy (E) of one photon:
E = h * ν
The Planck's constant (h) is approximately 6.63 x 10^(-34) joule-seconds.
E = (6.63 x 10^(-34) J·s) * (5.09 x 10^14 Hz)
≈ 3.37 x 10^(-19) J
Therefore, one photon of sodium's 589 nm radiation gives off approximately 3.37 x 10^(-19) joules of energy.
To calculate the energy given off by one photon of sodium, you can use the equation:
E = hf
Where:
E represents energy (in joules)
h represents Planck's constant (6.626 x 10^-34 J*s)
f represents frequency (in hertz)
To find the frequency, we can use the equation:
c = λf
Where:
c represents the speed of light (3 x 10^8 m/s)
λ represents the wavelength (589 nm) in meters
First, we need to convert the wavelength from nanometers (nm) to meters (m).
1 nm = 1 x 10^-9 m
So, 589 nm = 589 x 10^-9 m = 5.89 x 10^-7 m
Now, we can calculate the frequency using the equation:
c = λf
f = c / λ
f = (3 x 10^8 m/s) / (5.89 x 10^-7 m)
f ≈ 5.09 x 10^14 Hz
Using the frequency, we can now calculate the energy of one photon using the equation:
E = hf
E = (6.626 x 10^-34 J*s) x (5.09 x 10^14 Hz)
E ≈ 3.37 x 10^-19 J
Therefore, one photon of sodium emits approximately 3.37 x 10^-19 joules of energy.