Answer :
To find the frequency of blue light with a given wavelength, we can use the relationship between the speed of light [tex]\( c \)[/tex], wavelength [tex]\( λ \)[/tex], and frequency [tex]\( f \)[/tex]. The formula is:
[tex]\[ c = λ \times f \][/tex]
where:
- [tex]\( c \)[/tex] is the speed of light [tex]\( (3.0 \times 10^8 \, \text{m/s}) \)[/tex],
- [tex]\( λ \)[/tex] is the wavelength [tex]\( (4.83 \times 10^{-7} \, \text{m}) \)[/tex],
- [tex]\( f \)[/tex] is the frequency we need to find.
1. Rearrange the formula to solve for the frequency [tex]\( f \)[/tex]:
[tex]\[ f = \frac{c}{λ} \][/tex]
2. Substitute the given values into the formula:
[tex]\[ f = \frac{3.0 \times 10^8 \, \text{m/s}}{4.83 \times 10^{-7} \, \text{m}} \][/tex]
3. Calculate the division:
[tex]\[ f = \frac{3.0 \times 10^8}{4.83 \times 10^{-7}} \][/tex]
Now, we express the result in scientific notation. To do this, follow these steps:
4. Divide the numerators and isolate the powers of ten:
[tex]\[ f = \frac{3.0}{4.83} \times 10^{8 - (-7)} \][/tex]
5. Simplify the powers of ten:
[tex]\[ f = \frac{3.0}{4.83} \times 10^{15} \][/tex]
6. Perform the division for the coefficient:
[tex]\[ \frac{3.0}{4.83} \approx 0.620 (rounded value)\][/tex]
Now, to get the correct coefficient, let's multiply the numerator and denominator by 10 to clear the decimal:
[tex]\[ \frac{30}{48.3} \approx 0.620 \][/tex]
7. Refine the coefficient calculation to its accurate value (as given):
[tex]\[ 6.211180124223603 \][/tex]
So, combining the coefficient with the power of ten, we get:
[tex]\[ f \approx 6.211180124223603 \times 10^{14} \, \text{Hz}\][/tex]
Therefore, the frequency of blue light with a wavelength of [tex]\(4.83 \times 10^{-7} \, \text{m}\)[/tex] is approximately:
[tex]\[ \boxed{6.211180124223603 \times 10^{14} \, \text{Hz}} \][/tex]
So, the coefficient is [tex]\( 6.211180124223603 \)[/tex] and the exponent is [tex]\( 14 \)[/tex].
[tex]\[ c = λ \times f \][/tex]
where:
- [tex]\( c \)[/tex] is the speed of light [tex]\( (3.0 \times 10^8 \, \text{m/s}) \)[/tex],
- [tex]\( λ \)[/tex] is the wavelength [tex]\( (4.83 \times 10^{-7} \, \text{m}) \)[/tex],
- [tex]\( f \)[/tex] is the frequency we need to find.
1. Rearrange the formula to solve for the frequency [tex]\( f \)[/tex]:
[tex]\[ f = \frac{c}{λ} \][/tex]
2. Substitute the given values into the formula:
[tex]\[ f = \frac{3.0 \times 10^8 \, \text{m/s}}{4.83 \times 10^{-7} \, \text{m}} \][/tex]
3. Calculate the division:
[tex]\[ f = \frac{3.0 \times 10^8}{4.83 \times 10^{-7}} \][/tex]
Now, we express the result in scientific notation. To do this, follow these steps:
4. Divide the numerators and isolate the powers of ten:
[tex]\[ f = \frac{3.0}{4.83} \times 10^{8 - (-7)} \][/tex]
5. Simplify the powers of ten:
[tex]\[ f = \frac{3.0}{4.83} \times 10^{15} \][/tex]
6. Perform the division for the coefficient:
[tex]\[ \frac{3.0}{4.83} \approx 0.620 (rounded value)\][/tex]
Now, to get the correct coefficient, let's multiply the numerator and denominator by 10 to clear the decimal:
[tex]\[ \frac{30}{48.3} \approx 0.620 \][/tex]
7. Refine the coefficient calculation to its accurate value (as given):
[tex]\[ 6.211180124223603 \][/tex]
So, combining the coefficient with the power of ten, we get:
[tex]\[ f \approx 6.211180124223603 \times 10^{14} \, \text{Hz}\][/tex]
Therefore, the frequency of blue light with a wavelength of [tex]\(4.83 \times 10^{-7} \, \text{m}\)[/tex] is approximately:
[tex]\[ \boxed{6.211180124223603 \times 10^{14} \, \text{Hz}} \][/tex]
So, the coefficient is [tex]\( 6.211180124223603 \)[/tex] and the exponent is [tex]\( 14 \)[/tex].
