For two unknown particles A and B, graphs of ₁₀( ) versus ₁₀(v) are plotted, where is the de Broglie wavelength and v is the velocity. Both graphs yield straight lines. If the intercept on the ₁₀( ) axis for particle A is greater than that for particle B by 2 units, the ratio of the mass of particle B to the mass of particle A is ________.

Step-by-step solution

The de Broglie wavelength is given by the relation: = h mv Taking the base-10 logarithm on both sides, we get: ₁₀( ) = ₁₀ ( h m ) - ₁₀(v) This represents a straight line equation y = c + mx , where the y-axis is ₁₀( ) and the x-axis is ₁₀(v) . The y-intercept is given by: C = ₁₀ ( h m ) For particle A, the intercept is C_ A = ₁₀ ( h m_ A ) . For particle B, the intercept is C_ B = ₁₀ ( h m_ B ) . It is given that C_ A - C_ B = 2 . ₁₀ ( h m_ A ) - ₁₀ ( h m_ B ) = 2 Using the property of logarithms, ₁₀(x) - ₁₀(y) = ₁