Some diamonds appear yellow because they contain nitrogen, compounds that absorb purple light frequency 8.45×10¹⁰Hz calculate the wavelength in (nm and pm) of the absorbed
To calculate the wavelength of the absorbed light, we can use the equation:
wavelength = speed of light / frequency
Given:
Frequency of absorbed light = 8.45×10¹⁰ Hz
Speed of light (c) = 3×10^8 m/s
First, let's calculate the wavelength in nm (nanometers):
wavelength (in nm) = (speed of light / frequency) * 10⁹
wavelength (in nm) = (3×10⁸ m/s / 8.45×10¹⁰ Hz) * 10⁹
wavelength (in nm) = (3 × 10⁷ / 8.45) nm
wavelength (in nm) ≈ 3.554 nm
Now, let's convert the wavelength to pm (picometers):
wavelength (in pm) = wavelength (in nm) * 10³
wavelength (in pm) ≈ 3.554 nm * 10³
wavelength (in pm) ≈ 3554 pm
Therefore, the absorbed wavelength is approximately 3.554 nm (nanometers) and 3554 pm (picometers).
To calculate the wavelength in nanometers (nm) and picometers (pm) of the absorbed purple light frequency, we can use the formula:
wavelength (λ) = speed of light (c) / frequency (ν)
Given:
Frequency (ν) = 8.45×10¹⁰ Hz
The speed of light (c) is a constant which is approximately 3.00×10^8 meters per second (m/s).
Step 1: Convert the speed of light from meters per second (m/s) to nanometers per second (nm/s):
1 meter = 1,000,000,000 nanometers
So, 3.00×10^8 m/s = 3.00×10^8 × 1,000,000,000 nm/s = 3.00×10^17 nm/s
Step 2: Substitute the values into the formula to calculate the wavelength (λ):
λ = (3.00×10^17 nm/s) / (8.45×10^10 Hz)
Step 3: Perform the calculation to find the wavelength in nanometers:
λ = 3.55×10^6 nm
Step 4: Convert the wavelength from nanometers (nm) to picometers (pm):
1 nanometer (nm) = 1000 picometers (pm)
So, 3.55×10^6 nm = 3.55×10^6 × 1000 pm = 3.55×10^9 pm
Therefore, the wavelength of the absorbed purple light frequency in nanometers (nm) is approximately 3.55×10^6 nm, and in picometers (pm) is approximately 3.55×10^9 pm.
To calculate the wavelength of the absorbed light, we can use the formula:
\[ c = \lambda \cdot v \]
Where:
- c is the speed of light in a vacuum (approximately \( 3 \times 10^8 \) m/s),
- \( \lambda \) is the wavelength of the light in meters,
- v is the frequency of the light in Hz.
First, let's convert the frequency from Hz to s⁻¹:
\[ v = 8.45 \times 10^{10} \, \text{Hz} = 8.45 \times 10^{10} \, \text{s}^{-1} \]
Next, we can rearrange the formula to solve for \( \lambda \):
\[ \lambda = \frac{c}{v} \]
Substituting the values, we get:
\[ \lambda = \frac{3 \times 10^8 \, \text{m/s}}{8.45 \times 10^{10} \, \text{s}^{-1}} \]
Calculating this, we find the wavelength in meters. To convert it to nanometers (nm) or picometers (pm), we need to multiply by conversion factors:
- 1 meter = 10^9 nanometers (nm)
- 1 meter = 10^12 picometers (pm)
So, multiplying the wavelength in meters by these conversion factors, we get:
Wavelength in nanometers (nm) = \( \lambda \times 10^9 \) nm
Wavelength in picometers (pm) = \( \lambda \times 10^{12} \) pm
Now, let's calculate the wavelength:
\[ \lambda = \frac{3 \times 10^8 \, \text{m/s}}{8.45 \times 10^{10} \, \text{s}^{-1}} \]
\[ \lambda = 3.55 \times 10^{-3} \, \text{m} \]
Wavelength in nanometers (nm) = \( 3.55 \times 10^{-3} \times 10^9 \) nm
Wavelength in picometers (pm) = \( 3.55 \times 10^{-3} \times 10^{12} \) pm
Calculating these, we find:
Wavelength in nanometers (nm) = 355 nm
Wavelength in picometers (pm) = 3.55 x 10^5 pm
Therefore, the absorbed light has a wavelength of approximately 355 nm or 3.55 x 10^5 pm.