A typical gamma ray emitted from a nucleus during radioactive decay may have an energy of 736 keV. What is its wavelength?
A microwave oven produces electromagnetic radiation at λ = 12.1 cm and produces a power of 778 W. Calculate the number of microwave photons produced by the microwave oven each second
Gamma rays travel at the speed of light, 3*10^8 m/s. You can get the frequency f from the Planck relation
E = h*f
h is Planck's constant.
Get to know it.
Convert 736,000 eV to Joules.
1 eV = 1.6*10^-19 J
E = 736 keV = 1.18*10^-13 J
f = E/h = ___
wavelength = c/f = _____
1.1
To determine the wavelength of a gamma ray with energy 736 keV, we can use the equation:
E = hc/λ
Where:
E is the energy of the gamma ray = 736 keV = 736 x 10^3 eV
h is Planck's constant = 6.63 x 10^-34 J s
c is the speed of light = 3 x 10^8 m/s
λ is the wavelength
First, let's convert the energy to joules:
1 eV = 1.6 x 10^-19 J
736 x 10^3 eV = 736 x 10^3 x 1.6 x 10^-19 J = 1.18 x 10^-13 J
Now, we can rearrange the equation to solve for the wavelength:
λ = hc/E
λ = (6.63 x 10^-34 J s) / (1.18 x 10^-13 J)
λ = 5.61 x 10^-21 m
Therefore, the wavelength of a gamma ray emitted from the nucleus is approximately 5.61 x 10^-21 meters.
Now, let's calculate the number of microwave photons produced by the microwave oven each second.
The power of the microwave oven is given as 778 W, and we know that power is the energy per unit time. So, we can use the equation:
P = nE/t
Where:
P is the power = 778 W
n is the number of photons
E is the energy of each photon
t is the time = 1 second (since we want to find the number of photons per second)
Rearranging the equation to solve for the number of photons:
n = Pt/E
n = (778 W) x (1 second) / (λ x h x c)
Given that the wavelength (λ) is 12.1 cm = 12.1 x 10^-2 m, and using the values for Planck's constant (h) and the speed of light (c), we can calculate the number of photons:
n = (778 W) x (1 second) / (12.1 x 10^-2 m x 6.63 x 10^-34 J s x 3 x 10^8 m/s)
n ≈ 3.48 x 10^25 photons
Therefore, the number of microwave photons produced by the microwave oven each second is approximately 3.48 x 10^25 photons.
To find the wavelength of a gamma ray with an energy of 736 keV, we can use the equation:
E = hc/λ
Where E is the energy of the gamma ray, h is the Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (3 x 10^8 m/s), and λ is the wavelength.
First, we need to convert the energy from kilo-electron volts (keV) to joules (J):
E = 736 keV x (1.602 x 10^-16 J/eV) = 1.18 x 10^-13 J
Now, we can rearrange the equation to solve for λ:
λ = hc/E
λ = (6.626 x 10^-34 J·s) x (3 x 10^8 m/s) / (1.18 x 10^-13 J)
Calculating this equation gives us the wavelength of the gamma ray.
To calculate the number of microwave photons produced by a microwave oven each second, we can use the formula:
P = n * E
Where P is the power of the microwave oven (in watts), n is the number of photons produced per second, and E is the energy of each photon.
We need to convert the wavelength of the microwave radiation from centimeters (cm) to meters (m):
λ = 12.1 cm x (1 m/100 cm) = 0.121 m
Now, we can use the equation to calculate the energy of each photon:
E = hc/λ
E = (6.626 x 10^-34 J·s) x (3 x 10^8 m/s) / 0.121 m
Calculating this equation gives us the energy of each microwave photon.
Finally, we can rearrange the formula to solve for the number of photons (n):
n = P / E
n = 778 W / (energy of each photon)
Calculating this equation will give us the number of microwave photons produced by the microwave oven each second.