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Chapter 37: Q. 10 (page 1081)

Particle A has half the mass and twice the speed of particle B. Is the momentum P_A less than, greater than, or equal to P_B? Explain.

Short Answer

Expert verified

The momentum ofP_Ais greater than the momentum ofP_B.

Step by step solution

01

Given information

It is given that the mass of particle A is half the mass of B and Particle A has double the speed.

02

Explanation

In classical theory, they are deemed equal. While in the theory of relativity,

$\frac{p_{a}}{p_{b}} = \frac{γ_{p a} (0.5 m_{b}) (2 u_{b})}{γ_{p b} m_{b} u_{b}} = \frac{γ_{p a}}{γ_{p b}} > 1$

As $\frac{p_{a}}{p_{b}} > 1$

i.e $p_{a} > p_{b}$

Therefore,

The momentum ofP_Ais greater than the momentum ofP_B.

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Most popular questions from this chapter

An electron in a cathode-ray beam passes between $2.5 c m$ long parallel-plate electrodes that are $5.0 m m$ apart. A

$2.0 m T$ , $2.5 c m$ wide magnetic field is perpendicular to the electric field between the plates. The electron passes through the electrodes without being deflected if the potential difference between the plates is $600 V$ .

a. What is the electron’s speed?

b. If the potential difference between the plates is set to zero, what is the electron’s radius of curvature in the magnetic field?

Electrons pass through the parallel electrodes shown in $F I G U R E E X 37.9$ with a speed of role="math" localid="1649760459253" $5.0 \times 106 m / s$ . What magnetic field strength and direction will allow the electrons to pass through without being deflected? Assume that the magnetic field is confined to the region between the electrodes.

Figure 37.7 identified the wavelengths of four lines in the Balmer series of hydrogen.

a. Determine the Balmer formula n and m values for these wavelengths.

b. Predict the wavelength of the fifth line in the spectrum .

An alpha particle (a bare helium nucleus with $q = + 2 e$ ) acceler-ates across a $100 V$ potential difference, starting from rest. What is the particle’s kinetic energy in eV when it reaches the negative electrode? This question requires no mathematics beyond what you can do in your head.

Identify the element, the isotope, and the charge state of each atom in FIGURE $Q . 37.12$ . Give your answer in symbolic form, such as ⁴He⁺ or ⁸Be^-.

See all solutions

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