"Final Mission" is the 83rd episode of the science fictiontelevision seriesStar Trek: The Next Generation, and the ninth episode of the fourth season. After learning that he finally has been accepted into Starfleet Academy, Wesley Crusher welcomes Picard's invitation to accompany him on an away mission that could resolve a mining dispute on an arid world. But following a shuttle crash and a near disastrous search for water that leaves the captain near death, Wesley finds himself charged with the weighty responsibility of keeping both himself and Picard alive until a rescue team can locate them.
The Enterprise has traveled to the Pentarus system where Captain Picard (Patrick Stewart) must mediate a dispute among some miners on the fifth planet. Wesley Crusher (Wil Wheaton) receives word that he has been accepted to Starfleet Academy and, for his final mission, he will accompany Picard on his shuttle trip to Pentarus V. A distress call comes in from Gamilon V, where an unidentified vessel has entered orbit and is giving off lethal doses of radiation. Picard orders Riker to take the Enterprise to resolve that situation while he and Wesley travel in a shuttle sent by the miners. The shuttle is commanded by a seemingly unorthodox Captain Dirgo.
En route, one of the thrusters on Dirgo's ship is blown off and they are forced to crash-land on the surface of a harsh, desert-like moon. Though they are unharmed, the shuttle is beyond repair, and its communication systems and food replicators are disabled. Dirgo admits he has no emergency supplies on board, so they are forced to search for shelter and water. With his tricorder, Wesley identifies some caves and a potential source of water some distance away, and the three trek there. In a cave, they find a fountain-like water source, but it is protected by a crystalline forcefield. Dirgo attempts to use a phaser to destroy the field, but this only serves to cause a burst of energy to emanate from the fountain and cause a rock slide; Picard pushes Wesley out of the way but is severely injured in doing so.
Meanwhile, the Enterprise has arrived at Gamilon V, finding the unidentified ship is an abandoned garbage scow filled with radioactive waste. They attempt to send the barge into the Gamilon sun using attached thrusters to avoid getting the ship too close. A message is received informing the crew that the shuttle carrying Picard and Wesley never arrived and the miners are searching for them. When they attempt to engage the thrusters, one breaks away and compromises the structure of the barge. Commander Riker (Jonathan Frakes) then attempts the risky plan to take the barge into the sun themselves using the tractor beam, causing the crew to be exposed to the lethal radiation.
Picard has become weak from his injury, and Wesley asserts the need for water to be paramount. Wesley studies the fountain, noting that it is sensitive to the energy given off by phasers, but Dirgo bullies Wesley into more direct action, having them fire on the forcefield simultaneously with two phasers. Instead of disabling the force field, the energy envelops Dirgo and creates a crystalline shell around him, killing him. Meanwhile, the Enterprise, despite the growing lethal radiation levels on board, manages to get the barge headed into the sun and speeds off to help in the search for the shuttle.
Wesley continues to study the fountain. He determines that he can counteract the energy field protecting the fountain using his phaser and tricorder if he can act quickly enough. He fires the phaser at the fountain to attract the energy field that killed Dirgo, but uses the tricorder to send out a certain frequency to attempt to stop the field from attacking. He successfully brings down the field and gets the water.
Shortly thereafter, the Enterprise locates the wreckage of the mining shuttle, and soon Picard and Wesley are rescued. As Picard is carried from the cave, he tells Wesley that he will be missed.