To find the frequency of red light, we can use the relationship between the speed of light ([tex]\( c \)[/tex]), the wavelength ([tex]\( \lambda \)[/tex]), and the frequency ([tex]\( f \)[/tex]). This relationship is given by the equation:
[tex]\[ c = \lambda \cdot f \][/tex]
We are given:
- The speed of light, [tex]\( c = 3.0 \times 10^8 \)[/tex] meters per second.
- The wavelength of red light, [tex]\( \lambda = 6.5 \times 10^{-7} \)[/tex] meters.
Our goal is to find the frequency [tex]\( f \)[/tex]. We can rearrange the formula to solve for [tex]\( f \)[/tex]:
[tex]\[ f = \frac{c}{\lambda} \][/tex]
Substitute the given values into the equation:
[tex]\[ f = \frac{3.0 \times 10^8 \, \text{m/s}}{6.5 \times 10^{-7} \, \text{m}} \][/tex]
Now, divide:
[tex]\[ f = \frac{3.0 \times 10^8}{6.5 \times 10^{-7}} \][/tex]
To make the calculation simpler, we can express the numerator and the denominator in terms of powers of 10:
[tex]\[ f = \frac{3.0 \times 10^8}{6.5 \times 10^{-7}} = \frac{3.0}{6.5} \times 10^{8 - (-7)} = \frac{3.0}{6.5} \times 10^{15} \][/tex]
Carry out the division [tex]\( \frac{3.0}{6.5} \)[/tex]:
[tex]\[ \frac{3.0}{6.5} \approx 0.4615384615384615 \][/tex]
Multiplying by [tex]\( 10^{15} \)[/tex]:
[tex]\[ f \approx 0.4615384615384615 \times 10^{15} = 4.615384615384615 \times 10^{14} \, \text{Hz} \][/tex]
Rounding to a reasonable number of significant figures, we get:
[tex]\[ f \approx 4.6 \times 10^{14} \, \text{Hz} \][/tex]
Therefore, the frequency of red light with a wavelength of [tex]\( 6.5 \times 10^{-7} \)[/tex] meters is:
[tex]\[ \boxed{4.6 \times 10^{14} \, \text{Hz}} \][/tex]
This matches choice [tex]\( 4.6 \times 10^{14} \, \text{Hz} \)[/tex].
