Green light has a frequency of about 5.3Hz×1014Hz. Using the relationship c=fλ, find its wavelength in air.
lambda=speedlight/frequency.
To find the wavelength in air, we will use the relationship c = fλ, where c is the speed of light in a vacuum, f is the frequency, and λ is the wavelength.
The speed of light in a vacuum, c, is approximately 3.00 × 10^8 meters per second.
Given that the frequency, f, of green light is approximately 5.3 × 10^14 Hz, we can substitute these values into the equation c = fλ:
3.00 × 10^8 m/s = (5.3 × 10^14 Hz) λ
To find λ, we can rearrange the equation:
λ = (3.00 × 10^8 m/s) / (5.3 × 10^14 Hz)
Calculating this expression:
λ ≈ 5.66 × 10^(-7) meters
Therefore, the wavelength of green light in air is approximately 5.66 × 10^(-7) meters.
To find the wavelength of green light in air using the relationship c = fλ, where c represents the speed of light, f represents frequency, and λ represents wavelength, follow these steps:
Step 1: Identify the values given:
The frequency of green light is given as 5.3 x 10^14 Hz.
Step 2: Use the relationship c = fλ to solve for the wavelength:
Rearrange the equation to solve for λ:
λ = c / f
Step 3: Substitute the given values into the equation:
The speed of light, c, is approximately 3 x 10^8 meters per second (m/s).
The frequency, f, is given as 5.3 x 10^14 Hz.
λ = (3 x 10^8 m/s) / (5.3 x 10^14 Hz)
Step 4: Simplify the expression:
Divide the numerator and denominator by 10^14 to simplify the calculation.
λ = (3 x 10^8 m/s) / (5.3 x 10^14 Hz)
λ = (3/5.3) x (10^8/10^14) m
Step 5: Apply the rules of exponents:
When dividing with the same base (10 in this case), subtract the exponents.
λ = (3/5.3) x 10^(-6) m
Step 6: Convert the exponent to scientific notation:
Move the decimal point to the left to adjust the exponent to -6.
λ ≈ 0.566 x 10^(-6) m
Therefore, the approximate wavelength of green light in air is 0.566 x 10^(-6) meters, or in scientific notation, 5.66 x 10^(-7) meters.