Some instruments differentiate individual quanta of electromagnetic radiation based on their energies. Assume such an instrument has been adjusted to detect quanta that have 3.50× 10–16 J of energy. What is the wavelength of the detected radiation? Give your answer in nanometers.

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Now, let's calculate the wavelength of the detected radiation. We can use the equation E = hc/λ, where E is the energy of the photon, h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength.

Rearranging the equation, we have wavelength (λ) = hc/E.

Plugging in the values, we get:

λ = (6.626 x 10^-34 J·s * 3.00 x 10^8 m/s) / (3.50 × 10–16 J)

Calculating this, we find:

λ = (19.878 x 10^-26 J·m) / (3.50 × 10–16 J)
λ = 5.68 x 10^-10 m

To convert this to nanometers, we multiply by 10^9:

λ = 5.68 x 10^-10 m * 10^9 nm
λ = 5.68 nm

So, the wavelength of the detected radiation is approximately 5.68 nm.

To determine the wavelength of the detected radiation, we can use the equation:

E = hc/λ

Where:
E is the energy of the quanta (3.50×10^(-16) J),
h is the Planck's constant (6.62607015 × 10^(-34) J·s),
c is the speed of light (2.998 × 10^(8) m/s),
λ is the wavelength we want to find.

Now, let's rearrange the equation to solve for wavelength (λ):

λ = hc/E

Plugging in the values:

λ = (6.62607015 × 10^(-34) J·s * 2.998 × 10^(8) m/s) / (3.50 × 10^(-16) J)

λ = 5.68 × 10^(-9) m

To convert this to nanometers, we multiply by 10^(9):

λ = 5.68 × 10^(-9) m * 10^(9) nm/m = 5.68 nm

Therefore, the wavelength of the detected radiation is 5.68 nanometers.

To find the wavelength of the detected radiation, we can use the equation:

E = hc/λ

Where:
E = energy of the quantum
h = Planck's constant (6.626 × 10^(-34) Js)
c = speed of light in a vacuum (2.998 × 10^8 m/s)
λ = wavelength of the radiation

Rearranging the equation, we get:
λ = hc/E

Now, let's substitute the given values into the equation:

λ = (6.626 × 10^(-34) Js * 2.998 × 10^8 m/s) / (3.50 × 10^(-16) J)

Simplifying the equation:

λ = 18.448 × 10^(-34+8+16) / 3.50

λ = 18.448 × 10^(-2) / 3.50

λ = 5.27 × 10^(-2) meters

Since the answer should be given in nanometers, we convert meters to nanometers by multiplying by 10^9:

λ = 5.27 × 10^(-2) meters * 10^9 nm/m

λ = 5.27 × 10^7 nm

Therefore, the wavelength of the detected radiation is approximately 5.27 × 10^7 nanometers.

energy=plancksconstant*freq

wevelength= speedlight/freq