B2. What velocity D will an initially resting hydrogen atom acquire when emitting a photon corresponding to the first line of the Lyman series. ( h=6,62cdot 10^-34L_(K)cdot c,m_(H)=1,66cdot 10^-27kr,R=3,3cdot 10^15c^-1 (lambda =600nm) is incident on a thin glass wedge normal faces of the wedge if the liaht is

To find the velocity \( D \) that a hydrogen atom will acquire when emitting a photon corresponding to the first line of the Lyman series, we need to use the principles of energy conservation and the relationship between photon energy and momentum.<br /><br />The energy of the photon \( E \) is given by:<br />\[ E = \frac{hc}{\lambda} \]<br /><br />The momentum of the photon \( p \) is given by:<br />\[ p = \frac{h}{\lambda} \]<br /><br />The energy of the hydrogen atom before emitting the photon is essentially zero (since it is initially at rest). After emitting the photon, the hydrogen atom will have a kinetic energy \( K \) given by:<br />\[ K = \frac{1}{2}mv^2 \]<br /><br />Since energy is conserved, the energy of the photon will be equal to the kinetic energy of the hydrogen atom:<br />\[ \frac{hc}{\lambda} = \frac{1}{2}mv^2 \]<br /><br />We can solve for the velocity \( v \) (which we'll denote as \( D \) in the question):<br />\[ v = \sqrt{\frac{2hc}{m\lambda}} \]<br /><br />Now, let's plug in the given values:<br />- \( h = 6.62 \times 10^{-34} \, \text{J} \cdot \text{s} \)<br />- \( c = 3 \times 10^8 \, \text{m/s} \)<br />- \( m_H = 1.66 \times 10^{-27} \, \text{kg} \)<br />- \( \lambda = 600 \times 10^{-9} \, \text{m} \)<br /><br />\[ v = \sqrt{\frac{2 \times 6.62 \times 10^{-34} \, \text{J} \cdot \text{s} \times 3 \times 10^8 \, \text{m/s}}{1.66 \times 10^{-27} \, \text{kg} \times 600 \times 10^{-9} \, \text{m}}} \]<br /><br />\[ v = \sqrt{\frac{3.978 \times 10^{-34}}{9.96 \times 10^{-31}}} \]<br /><br />\[ v = \sqrt{4.00 \times 10^{-4}} \]<br /><br />\[ v \approx 0.632 \, \text{m/s} \]<br /><br />Therefore, the velocity \( D \) that the hydrogen atom will acquire when emitting a photon corresponding to the first line of the Lyman series is approximately \( 0.632 \, \text{m/s} \).