Given a single particle of mass m, the amount of energy E produced when all of its mass is converted to energy is given by Einstein's famous formula, E = m c?, where c = 2.9979 x 108 m/s is the speed of light. We also learned that the energy Ephoton of a single photon is related to its hc frequency f or wavelength A via Ephoton = hf = ne, where h = 6.626 x 10-34 m² kg/s is a %3D fundamental constant of nature called Planck's constant. In the electron + positron annihilation process discussed above, the two gamma-ray photons that are produced are identical. Compute the wavelength of one of these photons (in units of nm). Enter your answer as a decimal (NOT in scientific notation). You might check your answer against a chart of the EM spectrum to confirm that your answer is consistent with a gamma-ray wavelength.
Given a single particle of mass m, the amount of energy E produced when all of its mass is converted to energy is given by Einstein's famous formula, E = m c?, where c = 2.9979 x 108 m/s is the speed of light. We also learned that the energy Ephoton of a single photon is related to its hc frequency f or wavelength A via Ephoton = hf = ne, where h = 6.626 x 10-34 m² kg/s is a %3D fundamental constant of nature called Planck's constant. In the electron + positron annihilation process discussed above, the two gamma-ray photons that are produced are identical. Compute the wavelength of one of these photons (in units of nm). Enter your answer as a decimal (NOT in scientific notation). You might check your answer against a chart of the EM spectrum to confirm that your answer is consistent with a gamma-ray wavelength.
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Transcribed Image Text:The proton-proton chain is the multi-step process that powers the Sun via fusion of hydrogen into
helium. In the first step of the proton-proton chain, a positron is produced when two protons fuse
together (with one proton converting to a neutron). The emitted positron quickly collides with its
anti-particle, the electron. (Recall that the electron and positron have exactly the same mass, but
opposite electric charges.) The electron and positron then completely annihilate, converting all of
their rest mass into two gamma-ray photons.
Given a single particle of mass m, the amount of energy E produced when all of its mass is
converted to energy is given by Einstein's famous formula, E = m c?, where c = 2.9979 x 10° m/s is
%3D
the speed of light. We also learned that the energy Ephoton of a single photon is related to its
frequency f or wavelength A via Ephoton = hf =
hc
where h = 6.626 x 1034 m² kg/s is a
fundamental constant of nature called Planck's constant.
In the electron + positron annihilation process discussed above, the two gamma-ray photons that
are produced are identical. Compute the wavelength of one of these photons (in units of nm). Enter
your answer as a decimal (NOT in scientific notation). You might check your answer against a chart
of the EM spectrum to confirm that your answer is consistent with a gamma-ray wavelength.
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