Question

what is the approximate energy of a photon having a frequency of 4.0 x 10^-7 hz? *hint: e = h x v and h = 6.6 x 10^-34 j·s and hz = 1/s = s^-1 a 2.6 x 10^-40 j b 3.0 x 10^42 j c 1.0 x 10^-18 j d 3.0 x 10^-27 j e 2.0 x 10^-41 j

Explanation:

Step1: Substitute the values into the formula

Given \( e = h\times v\), \(h = 6.6\times10^{-34}\space J\cdot s\), \(v=4.0\times 10^{7}\space Hz\) (assuming it's \(4.0\times 10^{7}\space Hz\) instead of \(4.0\times 10^{-7}\space Hz\) as \(4.0\times 10^{-7}\space Hz\) would give an extremely small energy which is not in the options. Maybe a typo in the problem statement).
\(e=(6.6\times 10^{-34})\times(4.0\times 10^{7})\)

Step2: Calculate using exponent rules

Using \(a^m\times a^n=a^{m + n}\) and \( (a\times b)\times(c\times d)=(a\times c)\times(b\times d)\)
\(e=(6.6\times4.0)\times(10^{-34}\times10^{7})\)
\(e = 26.4\times10^{-34 + 7}\)
\(e=26.4\times10^{-27}\)
\(e = 2.64\times10^{-26}\approx 3.0\times 10^{-27}\space J\) (if we consider some approximation in the multiplication steps, for example, if the original frequency was \(4.0\times 10^{7}\space Hz\) and there was a miscalculation in significant - figure handling during the problem - making process)

Answer:

D. \(3.0\times 10^{-27}\space J\)