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+### Statement
+
+$10.1.4.$ [Insert the problem statement]
+
+### Solution
+
+### Statement
+
+10.1.4. What is the ratio of the trajectory radii of two electrons with kinetic energies $K_1$ and $K_2$ if a uniform magnetic field is perpendicular to their velocities?
+
+### Solution
+
+When an electron moves in a magnetic field, it experiences the Lorentz force, which causes it to move in a circular trajectory. The Lorentz force for an electron moving with velocity $v$ perpendicular to the magnetic field $B$ is:
+$$F = evB$$
+
+The centripetal acceleration for circular motion is described by the expression:
+$$a = \frac{v^2}{R}$$
+
+Let us write Newton's second law:
+$$evB = \frac{m_e v^2}{R}$$
+
+From this equation, we can express the trajectory radius $R$:
+$$R = \frac{m_e v}{eB} \quad (1)$$
+
+The kinetic energy of the first electron:
+$$K_1 = \frac{1}{2}m_e v^2$$
+
+From here, we express the velocity:
+$$v = \sqrt{\frac{2K_1}{m_e}}$$
+
+Substitute into (1):
+$$R_1 = \frac{m_e \sqrt{\frac{2K_1}{m_e}}}{eB} = \frac{\sqrt{2K_1 m_e}}{eB} \quad (2)$$
+
+Similarly, for the electron with kinetic energy $K_2$:
+$$R_2 = \frac{\sqrt{2K_2 m_e}}{eB} \quad (3)$$
+
+Let us take the ratio of the radii:
+$$\frac{R_1}{R_2} = \sqrt{\frac{K_1}{K_2}}$$
+
+#### Answer
+
+$$\frac{R_1}{R_2} = \sqrt{\frac{K_1}{K_2}}$$
+
+#### Answer
+
+[Insert a concise answer or boxed result]