91Ó°ÊÓ

The object absorbs a photon and changes its speed, implying that both its mass and momentum may change. By conservation of linear momentum, the total momentum before the collision (the sum of the object and photon momenta) must equal the total momentum after the collision. Before the collision, the object's momentum is \(m_0 \cdot v_0\) (where \(m_0\) is the original mass of the object and \(v_0\) is its original speed) and the photon's momentum is \(\frac{h}{\lambda}\) (where \(h\) is Planck’s constant and \(\lambda\) is the wavelength of the photon). After the collision, the object's momentum is \(m_1 \cdot v_1\) (where \(m_1\) is the mass of the object after collision and \(v_1\) is its speed after collision). Thus the conservation equation becomes: \(m_0 \cdot v_0 - \frac{h}{\lambda} = m_1 \cdot v_1\).

By algebraic manipulation, the ratio of the object's mass after the collision to its mass before the collision (\(m_1/m_0\)) can be determined: \(m_1/m_0 = \frac{v_0 - (h/(\lambda m_0))}{v_1}\). Replacing \(v_0\), \(v_1\), \(h\), and \(\lambda\) with their given values will provide the solution.

Since the object's speed decreases after the collision (from \(0.8c\) to \(0.6c\)), it is expected that its kinetic energy decreases as well. However, to confirm this, check the difference between the initial and final kinetic energies using the relativistic kinetic energy formula: \(K.E = mc^2 – m_0c^2\), where \(m\) is the relativistic mass, \(c\) is the speed of light, and \(m_0\) is the rest mass.