Answer :
Of course! Let's delve into finding the wavelength of a gamma ray with a frequency of [tex]\(1.0 \times 10^{19}\)[/tex] Hz and a given speed of light [tex]\( c = 3.0 \times 10^8 \)[/tex] m/s.
The relationship between the wavelength ([tex]\(\lambda\)[/tex]), the speed of light ([tex]\(c\)[/tex]), and the frequency ([tex]\(f\)[/tex]) is given by the following equation:
[tex]\[ \lambda = \frac{c}{f} \][/tex]
Plugging in the provided values:
[tex]\[ c = 3.0 \times 10^8 \, \text{m/s} \][/tex]
[tex]\[ f = 1.0 \times 10^{19} \, \text{Hz} \][/tex]
We can now substitute these values into the equation:
[tex]\[ \lambda = \frac{3.0 \times 10^8}{1.0 \times 10^{19}} \][/tex]
Next, we simplify the division:
[tex]\[ \lambda = 3.0 \times 10^8 \, \text{m/s} \div 1.0 \times 10^{19} \, \text{Hz} \][/tex]
This division of the coefficients gives:
[tex]\[ = 3.0 \div 1.0 = 3.0 \][/tex]
And the division of the powers of ten is:
[tex]\[ 10^8 \div 10^{19} = 10^{8-19} = 10^{-11} \][/tex]
Combining these results, we have:
[tex]\[ \lambda = 3.0 \times 10^{-11} \, \text{m} \][/tex]
Thus, the wavelength of the gamma ray is:
[tex]\[ 3.0 \times 10^{-11} \, \text{m} \][/tex]
The coefficient and the exponent are:
[tex]\[ (3.0, -11) \][/tex]
So, the wavelength of the gamma ray is [tex]\(3.0 \times 10^{-11}\)[/tex] meters.
The relationship between the wavelength ([tex]\(\lambda\)[/tex]), the speed of light ([tex]\(c\)[/tex]), and the frequency ([tex]\(f\)[/tex]) is given by the following equation:
[tex]\[ \lambda = \frac{c}{f} \][/tex]
Plugging in the provided values:
[tex]\[ c = 3.0 \times 10^8 \, \text{m/s} \][/tex]
[tex]\[ f = 1.0 \times 10^{19} \, \text{Hz} \][/tex]
We can now substitute these values into the equation:
[tex]\[ \lambda = \frac{3.0 \times 10^8}{1.0 \times 10^{19}} \][/tex]
Next, we simplify the division:
[tex]\[ \lambda = 3.0 \times 10^8 \, \text{m/s} \div 1.0 \times 10^{19} \, \text{Hz} \][/tex]
This division of the coefficients gives:
[tex]\[ = 3.0 \div 1.0 = 3.0 \][/tex]
And the division of the powers of ten is:
[tex]\[ 10^8 \div 10^{19} = 10^{8-19} = 10^{-11} \][/tex]
Combining these results, we have:
[tex]\[ \lambda = 3.0 \times 10^{-11} \, \text{m} \][/tex]
Thus, the wavelength of the gamma ray is:
[tex]\[ 3.0 \times 10^{-11} \, \text{m} \][/tex]
The coefficient and the exponent are:
[tex]\[ (3.0, -11) \][/tex]
So, the wavelength of the gamma ray is [tex]\(3.0 \times 10^{-11}\)[/tex] meters.
