What is the noble gas shorthand electron configuration of a tungsten atom?

So, you must write the electron configuration for tungsten, #"W"#, using the noble gas shorthand notation.

Tungsten is located in period 6, group 6 of the periodic table, and has an atomic number equal to #74#. This means that a neutral tungsten atom must have a total of #74# electrons surrounding its nucleus.

The first thing to do here is write the complete electron configuration, which will look like this

#"W: " 1s^2 2s^2 2p^6 3s^2 3p^6 3d^10 4s^2 4p^6 4d^10 5s^2 5p^6 4f^14 5d^4 6s^2#

Now, in order to write its noble gas shorthand, you need to first identify the noble gas that comes before tungsten in the periodic table.

In this case, that noble gas is xenon, #"Xe"#. Write out xenon's complete electron configuration next

#"Xe: " color(blue)(1s^2 2s^2 2p^6 3s^2 3p^6 3d^10 4s^2 4p^6 4d^10 5s^2 5p^6)#

Notice that the two electron configurations are identical for the first #54# electrons, which is the number of electrons that xenon has surrounding its nucleus.

This means that you can replace the first part of tungsten's configuration with that of xenon

#"W: "overbrace(color(blue)(1s^2 2s^2 2p^6 3s^2 3p^6 3d^10 4s^2 4p^6 4d^10 5s^2 5p^6))^(color(red)("xenon's electron configuration")) 4f^14 5d^4 6s^2#

You can write xenon's electron configuration as #["Xe"]#, which means that the noble gas shorthand notation for tungsten will be

#"W: " ["Xe"] 4f^14 5d^4 6s^2#