Answer:
[tex]\lambda = 390 nm[/tex]
Explanation:
Here we can use momentum conservation to find the initial wavelength of UV photon
so the equation for momentum conservation is given as
[tex]\frac{h}{\lambda} = m_1v_1 + m_2v_2[/tex]
we will have
[tex]v_1 = 1.15 \times 10^3 m/s[/tex]
[tex]m_1 = 1.67 \times 10^{-27} kg[/tex]
[tex]v_2 = -2.11 \times 10^6 m/s[/tex]
[tex]m_2 = 9.11 \times 10^{-31} kg[/tex]
so we will have
[tex]\frac{h}{\lambda} = (1.67 \times 10^{-27})(1.15 \times 10^3) - (9.11 \times 10^{-31})(2.11 \times 10^6)[/tex]
[tex]\frac{h}{\lambda} = -1.71 \times 10^{-27}[/tex]
[tex]\lambda = 390 nm[/tex]