Idea have been summoned.
Any type of decay, either that be uranium (U) strontium (Sr) thalium (Th), it is caused by an imbalance of radionuclide's (protons and neutrons) in the nucleus. This is not to confuse with an imbalance of protons and electrons which changes the charge. Basically the nucleus wants to be balanced (IE: x amount of protons and neutrons). If there's an imbalance of radionuclide's in the nucleus, it will emit them as forms of radiation.
There are three kinds of radiation that can be emitted by a radioactive isotope; alpha, beta, and gamma.
alpha radiation is the heaviest of the three, containing two protons and two neutrons, it is also the weakest in penetrating power because of how much mass it has. You may have also noticed that alpha radiation takes the form of a helium nucleus from its proton-neutron count, that's because alpha radiation is a helium nucleus!
Beta radiation is comprised of two forms beta plus (B+) and beta minus (B-). B+ is a positron and it's a very uncommon form of radiation. I think carbon-13 is an emitter of B+. B-, on the contrary, is an electron and is far more common/abundant across many radioactive isotopes. Th-204, is, approximately, a B- only emitter. U-238 is also a B- emitter.
Gamma radiation doesn't have any mass, and is light making it the most potent of the three.
Now to answer your questions:
"What happened to the respective electrons?" I think your confusing the difference of a helium nucleus and a helium atom, the helium nucleus indicates the number of neutrons and protons, it does not include the orbiting electrons of which the atom does includ. Alpha radiation is a helium nucleus not a helium atom
"Does this mean that each uranium atom, with 92 protons, entirely splits into 46 helium nucleei or does it release some number of helium nucleei leaving another element behind?" I highly recommend looking at the U-238 decay chain wikipedia article, it Illistrates how the decay chain process actually works. To answer your question, U-238 releases a helium nuclei during its decay chain process leaving strontium-xyz (forgot the isotope name).
"How does the concept of half life play into this?" Half-life states that for a given radioactive isotope how long does it take for that isotope to decay half of it's initial quantity. I think for uranium-238 it's 4.5 billion years or 9 billion years to fully deplete itself of any radiation.
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At the end of the day, a laptop is a laptop, and the cost difference between a $2000 brand new laptop and a $400 used laptop there really is no argument/justification to be made to buy a $2000 laptop in less-intensive tasks. Here's a better instance of your money: find a $400 laptop with semi-good performance (ryzen 3 or intel equivalent) put $1600 to a gaming computer and setup a virtual environment with a radeon or rtx gpu at your fingertips.