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The values of Planck's constant is 6.63 × 10–34 Js.
The velocity of light is 3.0 × 108 m s–1. Which value is closest to the wavelength in nanometres of a quantum of light with frequency of 8 × 1015 s–1?
- a)5 × 10–18
- b)4 × 101
- c)3 × 107
- d)2 × 10–25
Correct answer is option 'B'. Can you explain this answer?
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The values of Planck's constant is 6.63 × 10–34 Js.The velocity of li...
Given:
Planck's constant (h) = 6.63 × 10–34 Js
Velocity of light (c) = 3.0 × 108 m/s
Frequency of light (ν) = 8 × 1015 s–1
To find:
Wavelength of the light in nanometers
Solution:
The relationship between the frequency (ν), wavelength (λ), and velocity of light (c) is given by the equation:
c = νλ
Step 1: Rearranging the equation to solve for wavelength (λ):
λ = c / ν
Step 2: Substituting the given values into the equation:
λ = (3.0 × 10^8 m/s) / (8 × 10^15 s–1)
Step 3: Simplifying the expression:
λ = (3.0 × 10^8 / 8) × (10^15 / 1)
λ = 0.375 × 10^23 m
Step 4: Converting the wavelength to nanometers:
1 nm = 10^-9 m
λ (in nm) = (0.375 × 10^23 m) × (10^9 nm / 1 m)
λ (in nm) = 0.375 × 10^14 nm
Step 5: Expressing the wavelength in scientific notation:
λ (in nm) = 3.75 × 10^13 nm
Approximation:
The wavelength of the light is approximately 3.75 × 10^13 nm. Comparing this with the given options:
a) 5 × 10–18 nm
b) 4 × 101 nm
c) 3 × 107 nm
d) 2 × 10–25 nm
The closest value to 3.75 × 10^13 nm is option 'b' - 4 × 101 nm.
Planck's constant (h) = 6.63 × 10–34 Js
Velocity of light (c) = 3.0 × 108 m/s
Frequency of light (ν) = 8 × 1015 s–1
To find:
Wavelength of the light in nanometers
Solution:
The relationship between the frequency (ν), wavelength (λ), and velocity of light (c) is given by the equation:
c = νλ
Step 1: Rearranging the equation to solve for wavelength (λ):
λ = c / ν
Step 2: Substituting the given values into the equation:
λ = (3.0 × 10^8 m/s) / (8 × 10^15 s–1)
Step 3: Simplifying the expression:
λ = (3.0 × 10^8 / 8) × (10^15 / 1)
λ = 0.375 × 10^23 m
Step 4: Converting the wavelength to nanometers:
1 nm = 10^-9 m
λ (in nm) = (0.375 × 10^23 m) × (10^9 nm / 1 m)
λ (in nm) = 0.375 × 10^14 nm
Step 5: Expressing the wavelength in scientific notation:
λ (in nm) = 3.75 × 10^13 nm
Approximation:
The wavelength of the light is approximately 3.75 × 10^13 nm. Comparing this with the given options:
a) 5 × 10–18 nm
b) 4 × 101 nm
c) 3 × 107 nm
d) 2 × 10–25 nm
The closest value to 3.75 × 10^13 nm is option 'b' - 4 × 101 nm.
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The values of Planck's constant is 6.63 × 10–34 Js.The velocity of li...
E = hv = ch/λ ; and v = c/λ
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The values of Planck's constant is 6.63 × 10–34 Js.The velocity of light is 3.0 × 108 m s–1. Which value is closest to the wavelength in nanometres of a quantum of light with frequency of 8 × 1015 s–1?a)5 × 10–18 b)4 × 101c)3 × 107d)2 × 10–25Correct answer is option 'B'. Can you explain this answer?
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